外文翻译之滤波器外文原文及翻译
This invention relates to mechanical wave filters and more particularly to those which comprise one or more transverse members adapted for flexural vibration.An object of the invention is to reduce the minimum width of transmission band obtainable in a mechanical wave filter which employs a transverse flexural vibratory member.Other objects of the invention are to simplify the mechanical structure and reduce the cost of filters of this type.One form of mechanical wave filter comprises a central rod of acoustic material and one or more centrally located transverse members adapted to be set into flexural vibration when longitudinal vibrations are impressed upon an end of the rod. For a given rod, the width of the transmission band decreases as the mass of the transverse members is increased. Peaks of attenuation occur at the antiresonant frequencies of the transverse members, and these peaks are usually located close to the band limits to obtain sharp cut-offs. Heretofore, the transverse members have been made in the form of crossbars. The flexural antiresonance of abar is directly proportional to its width and inversely proportional to the square of its length. Since the antiresonant frequency is fixed, to increase the mass, and thereby narrow the band, the width of the bar may be increased by a factor K and its length increased at the same time by the square root of K. However, a point is reached at which the ratio of the width to the length is so large that the bar will no longer vibrate satisfactorily in the flexural mode. There is, therefore, a fairly definite limit on the minimum band width obtainable with filters using crossbars.In accordance with the present invention this limitation on minimum width of band is overcome by using a flexurally vibrating disc, mounted at its center, as the transverse member. By using a disc the mass is greatly increased and therefore a much narrower band may be obtained. A single disc will provide a peak of attenuation either above or below the band. Two discs located near the mid-point of the central rod and close together will provide a peak above and a peak below the band. The central rod has a small cross-sectional dimensions compared to its length, which isapproximately equal to a half wave-length at a frequency within the band.The nature of the invention will be more fully understood from the following detailed description and by reference to the accompanying drawing, in which like reference characters refer to similar parts and in which: Fig. 1 is a perspective view of a mechanical wave filter in accordance with the invention employing a single disc, andFig. 2 is a perspective view of a two-disc filter. Taking up the figures in more detail, Fig. 1 shows a mechanical wave filter in accordance with the invention comprising a central rod 1 of circular cross section and a transverse disc 2，both made of suitable acoustic material. The diameter A of the rod 1 is small compared to its length B, which is approximately a half wave-length at a cut-off frequency. The disc 2 has a diameter C and thickness D and is centrally mounted near the center of the rod 1. Longitudinal vibrations impressed upon an end of the bar 1 by a suitable driving device, represented diagrammatically by the box 3 shown in broken outline, will cause the disc 2 to vibrate in the flexural mode. Thelongitudinal vibrations of the rod 1 may be picked up at the other end of the filter by some suitable device, represented by the box 4 shown in broken outline. A peak of attenuation will occur at each frequency at which the disc 2 is antiresonant. The dimensions C and D of the disc 2 are, therefore, so proportioned that the first flexural antiresonance f l , given approximately by the following formula, occurs at a frequency, usually near aband limit, at which a peak is desired:121.872D f G = (1) where C and D are in centimeters, M is the density of the material, P is Poisson's ratio and Y is Young's modulus. If f l is on the lower side of the transmission band, the length B of the rod 1 is made approximately equal to a half wavelength at the upper cut-off frequency. If f l is above the band, B is made approximately equal to a half wave-length at the lower cut-off.If two peaks of attenuation are desired, one on either side of the band and close to the band limits, the structure shown in Fig. 2 may be used. The filtercomprises a central rod 1 and two transverse, centrally mounted discs 5 and 6, located close together one on either side of the center of the rod 1. One of the discs has its first flexural antiresonance at a frequency close to one limit of the band and the other disc has its first flexural antiresonance close to the other limit of the band. In this case the length B of the rod 1 is approximately equal to a half wavelength at the-band frequency.In mechanical filters of the type shown in Figs. 1 and 2, employing transverse impedance members, for a given rod 1 the width of the band decreases with an increase in the mass of the transverse members. The use of discs, such as 2, 5 and 6, for these members allows their mass to be greatly increased as compared, for example, with crossbars, and therefore a much narrower band may be obtained. The former limit on the minimum band width obtainable with filters using transverse members is thus greatly lowered in the disc-type filters of the present invention. Another distinct advantage of the disc-type filter is its mechanical simplicity. The filter may, for example, be made from a single piece of metal andcheaply turned out on a lathe.The image impedance Z of the filter, which should match the image impedance of the driving means at themid-band frequency, is given by the formula:Z Z = (2)where w is the angular frequency, j is the quadrantal operator, V is the velocity of propagation, equal to the square root of the ratio of Y to M, Z 0 is the characteristic impedance of the rod 1 and Z D is the impedance of the disc 2, for the filter of Fig.1, or the sum of the impedances of the two discs 5 and 6, for the filter of Fig.2. This image impedance is of a type which can be readily matched by a driver comprising a piezoelectric crystal attached at its end to an end of the rod 1.The filter will have a transmission band below, and one or more bands above, the principal band which has been here considered. These extraneous bands, if objectionable, may be eliminated by attenuation provided by the driving means, which should be designed to have a transmission band coinciding ，with the principal band of the mechanical filter. Thediscrimination of the filter may, of course, be increased dy connecting in tandem two or more sections of the type shown in Fig. 1 or Fig. 2.What is claimed is:1. A mechanical wave filter for transmitting a band of frequencies comprising a rod and a transverse disc both made of acoustic material, said rod having a length approximately equal to a half wave-length at a frequency within said band and said disc being centrally mounted near the center of said rod and adapted to be set into flexural vibration by longitudinal vibrations impressed upon an end of said rod and having a flexural antiresonance at a frequency close to one limit of said band.2. A filter in accordance with claim 1 in which said rod has a circular cross section.3. A filter in accordance with claim 1 in which the cross-sectional dimensions of said rod are small compared to its length.4. A filter in accordance with claim 1 in which said rod has a circular , cross section the diameter of which is small compared to its length.5. A filter in accordance with claim 1 in which said flexural antiresonance of said disc is its first.6. A mechanical wave filter for transmitting a band of frequencies comprising a rod and a transverse disc both made of acoustic material, said rod having a length approximately equal to a half wave-length at a frequency within said band and said disc being centrally mounted near the center of said rod and adapted to be set into flexural vibration by longitudinal vibrations impressed upon an end of said rod and having its first flexural antiresonance at a frequency on one side of said band and said rod having a length approximately equal to a half wave-length at the band limit on the other side of said band.7. A filter in accordance with claim 1 in which said flexural antiresonance of said disc is its first and said rod has a length approximately equal to a half wave-length at the other limit of said band.8. A mechanical wave filter for transmitting a band of frequencies comprising a rod and a transverse disc both made of acoustic material, said rod having a length approximately equal to a half wave-length at afrequency within said band and said disc being centrally mounted near the center of said rod and adapted to be set into flexural vibration by longitudinal vibrations impressed upon an end of said rod and having its first flexural antiresonance at a frequency on the upper side of said band and said rod having a length approximately equal to a half wave-length at the lower limit of said band.9. A filter in accordance with claim 1 in which said flexural antiresonance of said disc is its first and is located above said band and said rod has a length approximately equal to a half wave-length at the lower limit of said band.10. A mechanical wave filter for transmitting a band of frequencies comprising a rod and a transverse disc both made of acoustic material, said rod having a length approximately equal to a half wave-length at a frequency within said band and said disc being centrally mounted near the center of said rod and adapted to be set into flexural vibration by longitudinal vibrations impressed upon an end of said rod and having its first flexural antiresonance at a frequency on the lower sideof said band and said rod having a length approximately equal to a half wave-length at the upper limit of said band.11. A filter in accordance with claim 1 in which said flexural antiresonance of said disc is its first and is located below said band and said rod has a length approximately equal to a half wave-length at the upper limit of said band.12. A mechanical wave filter for transmitting a band of frequencies comprising a rod and two transverse discs, said rod having a length approximately equal to a half wave-length at a frequency within said band, said discs being centrally mounted, located close together near the center of said rod and adapted to be set into flexural vibration by longitudinal vibrations impressed upon an end of said rod, one of said discs having a flexural antiresonance at a frequency below said band and the other of said discs having a flexural antiresonance at a frequency above said band.13. A filter in accordance with claim 12 in which said discs are located one on either side of the center of said rod.rod has a length approximately equal to a half wave-length at the mid-band frequency.15. A filter in accordance with claim 12 in which said flexural antiresonances are located,respectively, close to the limits of said band.16. A filter in accordance with claim 12 in which said flexural antiresonance of said one disc is the only one occurring below said band and said flexural antiresonance of said other disc is its first.17. A mechanical wave filter for transmitting a band of frequencies comprising a rod and two transverse discs, said rod having a length approximately equal to a half wave-length at a frequency within said band, said discs being centrally mounted, located close together near the center of said rod and adapted to be set into flexural vibration by longitudinal vibrations impressed upon an end of said rod, one of said discs having its first flexural antiresonance at a frequency close to one limit of said band and the other of said discs having its first flexural antiresonance at a frequency close to the other limit of said band.rod has a length approximately equal to a half wave-length at the mid-band frequency.WARREN P. MASON.翻译本发明涉及机械滤波器，特别是那些包含一个或多个适应弯曲振动的横向构件。
图像处理中值滤波器中英文对照外文翻译文献
中英文资料对照外文翻译一、英文原文A NEW CONTENT BASED MEDIAN FILTERABSTRACTIn this paper the hardware implementation of a contentbased median filter suitabl e for real-time impulse noise suppression is presented. The function of the proposed ci rcuitry is adaptive; it detects the existence of impulse noise in an image neighborhood and applies the median filter operator only when necessary. In this way, the blurring o f the imagein process is avoided and the integrity of edge and detail information is pre served. The proposed digital hardware structure is capable of processing gray-scale im ages of 8-bit resolution and is fully pipelined, whereas parallel processing is used to m inimize computational time. The architecturepresented was implemented in FPGA an d it can be used in industrial imaging applications, where fast processing is of the utm ost importance. The typical system clock frequency is 55 MHz.1. INTRODUCTIONTwo applications of great importance in the area of image processing are noise filtering and image enhancement [1].These tasks are an essential part of any image pro cessor,whether the final image is utilized for visual interpretation or for automatic an alysis. The aim of noise filtering is to eliminate noise and its effects on the original im age, while corrupting the image as little as possible. To this end, nonlinear techniques (like the median and, in general, order statistics filters) have been found to provide mo re satisfactory results in comparison to linear methods. Impulse noise exists in many p ractical applications and can be generated by various sources, including a number of man made phenomena, such as unprotected switches, industrial machines and car ign ition systems. Images are often corrupted by impulse noise due to a noisy sensor or ch annel transmission errors. The most common method used for impulse noise suppressi on n forgray-scale and color images is the median filter (MF) [2].The basic drawback o f the application of the MF is the blurringof the image in process. In the general case,t he filter is applied uniformly across an image, modifying pixels that arenot contamina ted by noise. In this way, the effective elimination of impulse noise is often at the exp ense of an overalldegradation of the image and blurred or distorted features[3].In this paper an intelligent hardware structure of a content based median filter (CBMF) suita ble for impulse noise suppression is presented. The function of the proposed circuit is to detect the existence of noise in the image window and apply the corresponding MFonly when necessary. The noise detection procedure is based on the content of the im age and computes the differences between the central pixel and thesurrounding pixels of a neighborhood. The main advantage of this adaptive approach is that image blurrin g is avoided and the integrity of edge and detail information are preserved[4,5]. The pro posed digital hardware structure is capable of processing gray-scale images of 8-bitres olution and performs both positive and negative impulse noise removal. The architectt ure chosen is based on a sequence of four basic functional pipelined stages, and parall el processing is used within each stage. A moving window of a 3×3 and 5×5-pixel im age neighborhood can be selected. However, the system can be easily expanded to acc ommodate windows of larger sizes. The proposed structure was implemented using fi eld programmable gate arrays (FPGA). The digital circuit was designed, compiled and successfully simulated using the MAX+PLUS II Programmable Logic Development S ystem by Altera Corporation. The EPF10K200SFC484-1 FPGA device of the FLEX1 0KE device family was utilized for the realization of the system. The typical clock fre quency is 55 MHz and the system can be used for real-time imaging applications whe re fast processing is required [6]. As an example,the time required to perform filtering of a gray-scale image of 260×244 pixels is approximately 10.6 msec.2. ADAPTIVE FILTERING PROCEDUREThe output of a median filter at a point x of an image f depends on the values of t he image points in the neighborhood of x. This neighborhood is determined by a wind ow W that is located at point x of f including n points x1, x2, …, xn of f, with n=2k+1. The proposed adaptive content based median filter can be utilized for impulse noisesu p pression in gray-scale images. A block diagram of the adaptive filtering procedure is depicted in Fig. 1. The noise detection procedure for both positive and negative noise is as follows:(i) We consider a neighborhood window W that is located at point x of the image f. Th e differences between the central pixel at point x and the pixel values of the n-1surr ounding points of the neighborhood (excluding thevalue of the central pixel) are co mputed.(ii) The sum of the absolute values of these differences is computed, denoted as fabs(x ). This value provides ameasure of closeness between the central pixel and its su rrounding pixels.(iii) The value fabs(x) is compared to fthreshold(x), which is anappropriately selected positive integer threshold value and can be modified. The central pixel is conside red to be noise when the value fabs(x) is greater than thethreshold value fthresho d(x).(iv) When the central pixel is considered to be noise it is substituted by the median val ue of the image neighborhood,denoted as fk+1, which is the normal operationof the median filter. In the opposite case, the value of the central pixel is not altered and the procedure is repeated for the next neighborhood window.From the noised etection scheme described, it should be mentioned that the noise detection level procedure can be controlled and a range of pixel values (and not only the fixedvalues of 0 and 255, salt and pepper noise) is considered asimpulse noise.In Fig. 2 the results of the application of the median filter and the CBMF in the gray-sca le image “Peppers” are depicted.More specifically, in Fig. 2(a) the original,uncor rupted image“Peppers” is depicted. In Fig. 2(b) the original imagedegraded by 5% both positive and negative impulse noise isillustrated. In Figs 2(c) and 2(d) the resultant images of the application of median filter and CBMF for a 3×3-pixel win dow are shown, respectively. Finally, the resultant images of the application of m edian filter and CBMF for a 5×5-pixelwindow are presented in Figs 2(e) and 2(f). It can be noticed that the application of the CBMF preserves much better edges a nddetails of the images, in comparison to the median filter.A number of different objective measures can be utilized forthe evaluation of these results. The most wi dely used measures are the Mean Square Error (MSE) and the Normalized Mean Square Error (NMSE) [1]. The results of the estimation of these measures for the two filters are depicted in Table I.For the estimation of these measures, the result ant images of the filters are compared to the original, uncorrupted image.From T able I it can be noticed that the MSE and NMSE estimatedfor the application of t he CBMF are considerably smaller than those estimated for the median filter, in all the cases.Table I. Similarity measures.3. HARDWARE ARCHITECTUREThe structure of the adaptive filter comprises four basic functional units, the mo ving window unit , the median computation unit , the arithmetic operations unit , and th e output selection unit . The input data of the system are the gray-scale values of the pi xels of the image neighborhood and the noise threshold value. For the computation of the filter output a3×3 or 5×5-pixel image neighborhood can be selected. Image input d ata is serially imported into the first stage. In this way,the total number of the inputpin s are 24 (21 inputs for the input data and 3 inputs for the clock and the control signalsr equired). The output data of the system are the resultant gray-scale values computed f or the operation selected (8pins).The moving window unit is the internal memory of the system,used for storing th e input values of the pixels and for realizing the moving window operation. The pixel values of the input image, denoted as “IMAGE_INPUT[7..0]”, areimported into this u nit in serial. For the representation of thethreshold value used for the detection of a no Filter Impulse noise 5% mse Nmse(×10-2) 3×3 5×5 3×3 5×5Median CBMF 57.554 35.287 130.496 84.788 0.317 0.194 0.718 0.467ise pixel 13 bits are required. For the moving window operation a 3×3 (5×5)-pixel sep entine type memory is used, consisting of 9 (25)registers. In this way,when the windoP1 P2 P3w is moved into the next image neighborhood only 3 or 5 pixel values stored in the memory are altered. The “en5×5” control signal is used for the selection of the size of th e image window, when“en5×5” is equal to “0” (“1”) a 3×3 (5×5)-pixel neighborhood is selected. It should be mentioned that the modules of the circuit used for the 3×3-pix el window are utilized for the 5×5-pixel window as well. For these modules, 2-to-1mu ltiplexers are utilized to select the appropriate pixel values,where necessary. The mod ules that are utilized only in the case of the 5×5-pixel neighborhood are enabled by th e“en5×5” control signal. The outputs of this unit are rows ofpixel values (3 or 5, respe ctively), which are the inputs to the median computation unit.The task of the median c omputation unit is to compute themedian value of the image neighborhood in order to substitutethe central pixel value, if necessary. For this purpose a25-input sorter is utili zeed. The structure of the sorter has been proposed by Batcher and is based on the use of CS blocks. ACS block is a max/min module; its first output is the maximumof the i nputs and its second output the minimum. The implementation of a CS block includes a comparator and two 2-to-1 multiplexers. The outputs values of the sorter, denoted a s “OUT_0[7..0]”…. “OUT_24[7..0]”, produce a “sorted list” of the 25 initial pixel val ues. A 2-to-1 multiplexer isused for the selection of the median value for a 3×3 or 5×5-pixel neighborhood.The function of the arithmetic operations unit is to computethe value fabs(x), whi ch is compared to the noise threshold value in the final stage of the adaptive filter.The in puts of this unit are the surrounding pixel values and the central pixelof the neighb orhood. For the implementation of the mathematical expression of fabs(x), the circuit of this unit contains a number of adder modules. Note that registers have been used to achieve a pipelined operation. An additional 2-to-1 multiplexer is utilized for the selec tion of the appropriate output value, depending on the “en5×5” control signal. From th e implementation point of view, the use of arithmetic blocks makes this stage hardwar e demanding.The output selection unit is used for the selection of the appropriateoutput value of the performed noise suppression operation. For this selection, the corresponding no ise threshold value calculated for the image neighborhood,“NOISE_THRES HOLD[1 2..0]”,is employed. This value is compared to fabs(x) and the result of the comparison Classifies the central pixel either as impulse noise or not. If thevalue fabs(x) is greater than the threshold value fthreshold(x) the central pixel is positive or negative impulse noise and has to be eliminated. For this reason, the output of the comparison is used as the selection signal of a 2-to-1 multiplexer whose inputs are the central pixel and the c orresponding median value for the image neighborhood. The output of the multiplexer is the output of this stage and the final output of the circuit of the adaptive filter.The st ructure of the CBMF, the computation procedure and the design of the four aforeme n tioned units are illustrated in Fig. 3.ImagewindoeFigure 1: Block diagram of the filtering methodFigure 2: Results of the application of the CBMF: (a) Original image, (b) noise corrupted image (c) Restored image by a 3x3 MF, (d) Restored image by a 3x3 CBMF, (e) Restored image by a 5x5 MF and (f) Restored image by a 5x5 CBMF.4. IMPLEMENTATION ISSUESThe proposed structure was implemented in FPGA,which offer an attractive com bination of low cost, high performance and apparent flexibility, using the software pa ckage+PLUS II of Altera Corporation. The FPGA used is the EPF10K200SFC484-1 d evice of the FLEX10KE device family,a device family suitable for designs that requir e high densities and high I/O count. The 99% of the logic cells(9965/9984 logic cells) of the device was utilized to implement the circuit . The typical operating clock frequ ency of the system is 55 MHz. As a comparison, the time required to perform filtering of a gray-scale image of 260×244 pixelsusing Matlab® software on a Pentium 4/2.4 G Hz computer system is approximately 7.2 sec, whereas the corresponding time using h ardware is approximately 10.6 msec.The modification of the system to accommodate windows oflarger sizes can be done in a straightforward way, requiring onlya small nu mber of changes. More specifically, in the first unit the size of the serpentine memory P4P5P6P7P8P9SubtractorarryMedianfilteradder comparatormuitiplexerf abc(x)valueand the corresponding number of multiplexers increase following a square law. In the second unit, the sorter module should be modified,and in the third unit the number of the adder devicesincreases following a square law. In the last unit no changes are requ ired.5. CONCLUSIONSThis paper presents a new hardware structure of a content based median filter, ca pable of performing adaptive impulse noise removal for gray-scale images. The noise detection procedure takes into account the differences between the central pixel and th e surrounding pixels of a neighborhood.The proposed digital circuit is capable ofproce ssing grayscale images of 8-bit resolution, with 3×3 or 5×5-pixel neighborhoods as op tions for the computation of the filter output. However, the design of the circuit is dire ctly expandableto accommodate larger size image windows. The adaptive filter was d eigned and implemented in FPGA. The typical clock frequency is 55 MHz and the sys tem is suitable forreal-time imaging applications.REFERENCES[1] W. K. Pratt, Digital Image Processing. New York: Wiley,1991.[2] G. R. Arce, N. C. Gallagher and T. Nodes, “Median filters:Theory and applicat ions,” in Advances in ComputerVision and Image Processing, Greenwich, CT: JAI, 1986.[3] T. A. Nodes and N. C. Gallagher, Jr., “The output distributionof median type filte rs,” IEEE Transactions onCommunications, vol. COM-32, pp. 532-541, May1984.[4] T. Sun and Y. Neuvo, “Detail-preserving median basedfilters in imageprocessing,” Pattern Recognition Letters,vol. 15, pp. 341-347, Apr. 1994.[5] E. Abreau, M. Lightstone, S. K. Mitra, and K. Arakawa,“A new efficient approachfor the removal of impulsenoise from highly corrupted images,” IEEE Transa ctionson Image Processing, vol. 5, pp. 1012-1025, June 1996.[6] E. R. Dougherty and P. Laplante, Introduction to Real-Time Imaging, Bellingham:SPIE/IEEE Press, 1995.二、英文翻译基于中值滤波的新的内容摘要在本设计中的提出了基于中值滤波的硬件实现用来抑制脉冲噪声的干扰。
外文文献翻译译稿和原文
外文文献翻译译稿1卡尔曼滤波的一个典型实例是从一组有限的，包含噪声的，通过对物体位置的观察序列（可能有偏差）预测出物体的位置的坐标及速度。
在很多工程应用（如雷达、计算机视觉）中都可以找到它的身影。
同时，卡尔曼滤波也是控制理论以及控制系统工程中的一个重要课题。
例如，对于雷达来说，人们感兴趣的是其能够跟踪目标。
但目标的位置、速度、加速度的测量值往往在任何时候都有噪声。
卡尔曼滤波利用目标的动态信息，设法去掉噪声的影响，得到一个关于目标位置的好的估计。
这个估计可以是对当前目标位置的估计（滤波），也可以是对于将来位置的估计（预测），也可以是对过去位置的估计（插值或平滑）。
命名[编辑]这种滤波方法以它的发明者鲁道夫.E.卡尔曼（Rudolph E. Kalman）命名，但是根据文献可知实际上Peter Swerling在更早之前就提出了一种类似的算法。
斯坦利。
施密特（Stanley Schmidt）首次实现了卡尔曼滤波器。
卡尔曼在NASA埃姆斯研究中心访问时，发现他的方法对于解决阿波罗计划的轨道预测很有用，后来阿波罗飞船的导航电脑便使用了这种滤波器。
关于这种滤波器的论文由Swerling（1958）、Kalman (1960)与Kalman and Bucy（1961）发表。
目前，卡尔曼滤波已经有很多不同的实现。
卡尔曼最初提出的形式现在一般称为简单卡尔曼滤波器。
除此以外，还有施密特扩展滤波器、信息滤波器以及很多Bierman, Thornton开发的平方根滤波器的变种。
也许最常见的卡尔曼滤波器是锁相环，它在收音机、计算机和几乎任何视频或通讯设备中广泛存在。
以下的讨论需要线性代数以及概率论的一般知识。
卡尔曼滤波建立在线性代数和隐马尔可夫模型（hidden Markov model）上。
其基本动态系统可以用一个马尔可夫链表示，该马尔可夫链建立在一个被高斯噪声（即正态分布的噪声）干扰的线性算子上的。
系统的状态可以用一个元素为实数的向量表示。
电子信息工程专业外文翻译--滤波器
外文原文一、a question for study or discussion1．Research background and purpose1.1 conceptualizeElliptic filter (Elliptic filter), also known as the Call filter (Cauer filter), is in the passband and stopband ripple of a filter. Elliptic filter when compared to other types of filters, in order under the same conditions with minimal fluctuations in the passband and stopband. Same as its wave in passband and stopband, which distinguish it from the Butterworth filter with flat passband and stopband and flat passband and the stopband ripple or resistance with flat, cut than the snow filter passband ripple.A low-pass filter with a frequency response range of the ellipse：Four-order low-pass elliptic filter frequency response。
1.2 scientific researchIn the low-frequency (600Hz=500KHz) commonly used in band-pass filter, large LC filters, poor stability, stability of Crystal filters, but can only be made of narrow-band filter, bad shock and vibration resistance. Active filters are small, but stability and decay characteristics are often poor, and debugging easy. Ceramic filter is poor and low-frequency seismic performance of low temperature coefficient. And than snow filter Butterworth filter transfer function is a polynomial divided by a constant, for the whole network, all zeros in infinite, only infinite stopband attenuation is infinite, and the elliptic filter in both with zeros and poles on the limited frequency. Zero ripple in the passband, that it has a minimum across the passband and stopband ripple, This is distinguished from Butterworth filter with flat passband and stopband。
DSP滤波器中英文对照外文翻译文献
中英文对照外文翻译文献(文档含英文原文和中文翻译)译文:GA算法优化IIR滤波器的设计摘要本文提出了运用遗传算法(GA)来优化无限脉冲响应数字滤波器(IIR)的设计。
IIR滤波器本质上是一个递归响应的数字滤波器。
由于IIR 数字滤波器的表面误差通常是非线性的和多峰的，而全局优化技术需要避免局部最小值。
本文提出了启发式方式来设计IIR滤波器。
GA是组合优化问题中一种功能强大的全局优化算法，该论文发现IIR数字滤波器的最佳系数可以通过GA 优化。
该设计提出低通和高通IIR数字滤波器的设计，以提供过渡频带的估计值。
结果发现，所计算出的值比可用于过滤器的在MATLAB设计FDA工具更优化。
举个例子，采用的仿真结果表明在过渡带和均方误差(MSE)的改善。
零极点的位置也被提出来用来描述系统的的稳定性，以便将结果与模拟退火(SA)的方法相比较。
关键词：数字滤波器;无限冲激响应(IIR);遗传算法(GA);优化1.说明在过去的几十年中的数字信号处理(DSP)领域已经成长太重要的理论和技术。
在DSP中，有两个重要的类型系统。
第一类型的系统是执行信号滤波的时域，因此它被称为数字滤波器。
第二类型的系统提供的信号表示频域，被称为频谱分析仪。
数字滤波是DSP的最有力的工具之一。
数字滤波器能够性能规格，最好的同时也是极其困难的，而且不可能的是，先用模拟滤波器实现。
另外，数字滤波器的特性，可以很容易地在软件控制下发生变化。
数字滤波器被分类为有限持续时间脉冲响应(FIR)滤波器或无限持续时间脉冲响应(IIR)滤波器，这取决于该系统的脉冲响应的形式。
在FIR系统中，脉冲响应序列是有限的持续时间，即，它具有非零项的数量有限。
数字无限脉冲响应(IIR)滤波器通常可以提供比其等效有限脉冲响应(FIR)滤波器更好的性能和更少的计算成本，并已成为越来越感兴趣的目标。
但是，由于IIR滤波器的误差表面通常是非线性的，多式联运，传统的基于梯度的设计方法可以很容易地陷入错误的表面。
毕业设计论文 外文文献翻译 微波滤波器的发展及发展前景 中英文对照
The development of microwave filters and development prospectsThe development of microwave filtersIn 1917, the U.S. and German scientists were invented the LC filters, the following year led the United States first multiplexing systems to appear. The 1950 s no filter more mature. Since the s with the computer technology, integrated process and material industry development, the filter development on a new level, low power consumption, high precision and toward, small volume, multi-function, stability and low price can be high and effort, including small volume, multi-function, high precision, high stability can be the main attack direction of the 70 s. Cause RC active filter, digital filters, switch capacitance filter and the charge transfer of the rapid development of the filter, by the late 70's, the above several filter monolithic integration has been developed and applied. In the 80 s, specialized in all kinds of new type filter research, and strive to improve performance and gradually expand the scope of application. In the 90 s to now mainly devotes to the of all kinds filter used in all kinds of filter development and the development of all kinds of products. Of course, to filter the research continues to itself.Our country wide use filter is 50 s, when it was used for filtering and words road way filter. After a half century of development, our country filter in the development, the production and the application has set up a file in the development step, the single due to the lack of specialized research institutions, integration process and material industry in our country, yes to keep up with the development of many new filter application and international development for a short distance.Filter is a kind of two-port network, it has to choose the characteristics of frequency, that can make some frequency smoothly through, but to other frequency is to stop. Filter is radio technology in the center of the many design problems, at present in radar and microwave because, communication, and other departments, many frequency is becoming more and more common, to work the requirements of space frequency also increase, so need to a large number of filter.The merits of the filter directly determine product quality, so to filter in the research and production has always for all countries take seriously. In 1917, theUnited States and Germany scientists were invented the LC filters, the following year led the United States first multiplexing systems to appear. In the 1950 s, passive filter more mature. Since the s with the computer technology, integrated process and material industry development, the development of the filter on a new level, low power consumption, high precision and toward, small volume, multi-function, stable and reliable and inexpensive, of which direction small size, multi-function, high precision, stable and reliable in the 70 s as the main attack direction in the future, leading to the RC active filter, digital filters, switch capacitance filter and the charge transfer machine etc all kinds of filter of rapid development. By the late 70's, the above several filter monolithic integration has been developed and get the application. In the 80 s, mainly specialized in all kinds of new type filter research, and strive to improve performance and gradually expand the scope of application. Since the 90 s the main work to make all kinds of filter used in all kinds of product development and research. Of course, to filter the research continues to itself.The application of microwave solid device to filter development has a certain role as parameters, amplifiers, microwave solid times frequency of an, microwave solid mixers, kind of device is more work is needed, the frequency of corresponding filter. With the rapid development of the integrated circuit, in recent years, the composition of the electronic circuit completely changed, electronic equipment is miniaturization. Originally for process simulation signal is indispensable LC type filter, in the low frequency part, will gradually be active filter and ceramic filter replaced; In the high frequency part also appeared a lot of new type filter, for example: spiral oscillator filter, microstrip filter, pay refers to type filter, etc. Although they design methods have their own special place, but these design method is still low frequency "synthesis filter design" as the foundation, and evolving out of it.The prospect of microwave filtersMicrowave filter microwave field is key components, widely used in communication, radar system, is an indispensable part of the field. At present, the technology, the rapid development of microwave filters is a very active, branch, in recent years, major progress and development trend are as follows:(1) from individual applied to general application. If you consider that a microwave cavity resonator is a microwave filters the basic units of the word, can say it is also in the microwave technology study of one of the basic subject. But in fact, or early because the task of microwave equipment is lower, or because of the microwave filters analysis, design and manufacture all very hard, so, when people would direct application single lumen resonators, and less likely to put them into a more excellent properties of combination of microwave filters. But with microwave theory and technology development, the microwave band of electronic equipment, the increase of the spectrum of the crowded, and against the commonly used electronic technology to filter in the application of microwave breadth and depth on the great progress(2) design method from numerous to Jane, from rough to accurately. In the past people with wave method to use some simple microwave filter structure analysis and design, already feel very difficult. And now, can complete application of modern network integrated theoretical results, smoothly carry on various microwave filters, and a comprehensive electronic computer work out of a lot of the curves and data are available, simplified calculation, artificial improve the design precision;(3) various forms and components change, standardization. Due to the applications of design and manufacturing technology progress, microwave filters already from the few several varieties development plan to hundreds of thousands of a structure types ten. Some commonly used modular structure has and standardization. Printing circuit type or microwave integrated circuits type microwave filters also started to widely developed;(4) and other active or passive microwave components and devices is increasingly close combination. Now, microwave filters has become a passive microwave components of one of leading role, it not only can complete the task of itself, and can take the place of some other microwave components of the function, or the other microwave components as microwave filters structure to design;(5) of new materials for microwave filters. Microwave material progress and its application in microwave filters and greatly enhance the performance of the filter.Such as microwave ferrite, ferroelectric, plasma, superconductivity has started to successfully used in(6) the high-speed and automation tuned. As is known to all, when microwave single lumen resonators tuning already quite difficult, not to mention the DuoGe resonators combination of the filter. But now has to microwave filters can be fast the electricity, for example have iron garnet tone filters and transfiguration magnetic tube electric adjustable filter is the best examples;(7) to the new band march. People the millimeter wave and the millimeter wave filter is increasing interest in. Developing the new band of filters, in addition to the development of the existing technology performance band outside, still widely quoted optical achievements, such as the law in a clap, cloth Saul resonator and other various filters and directional coupling the structure has been quoted as saying to come over from the optics. As can be expected, along with the new power source and the development of the transmission line, these new band the development of the filter will be more active.Our country at present the application of various filter ratioour country's existing types and filter covered frequency has basically satisfy the existing various telecom equipment. From the overall, our country active filter development than a passive filter and have not yet been slow of production and application. From the following production application proportion of various types of filters can be seen, the application of the: LC filters accounted for 50%; Crystal filter accounted for 20%; Mechanical filter accounted for 15%; Ceramic filter harmonic surface each accounted for 1%; The rest accounted for 13% of all kinds of filter. From the application scale, electronic products in China to realize the large-scale integrated, filter integration is still a important topic.along with the development of the electronic industry to filter, the performance requirements of more and more high, function more and more, and asked them to integration development direction. Our country filter development and production of the above requirements and far, in order to reduce that gap, electronic engineering and scientific and technological personnel have important historical responsibility.微波滤波器的发展及发展前景微波滤波器的发展1917年美国和德国科学家分别发明了LC滤波器，次年导致了美国第一个多路复用系统的出现。
外文翻译--数字滤波器的仿真与实现
毕业设计(论文)外文资料翻译院系电子信息工程专业电子信息工程学生姓名班级学号外文出处百度文库附件：1.外文资料翻译译文（约3000汉字）；2.外文资料原文(与课题相关的1万印刷符号左右)。
英文原文The simulation and the realization of the digital filter With the information age and the advent of the digital world, digital signal processing has become one of today's most important disciplines and door technology. Digital signal processing in communications, voice, images, automatic control, radar, military, aerospace, medical and household appliances, and many other fields widely applied. In the digital signal processing applications, the digital filter is important and has been widely applied.1、figures Unit on :Analog and digital filtersIn signal processing, the function of a filter is to remove unwanted parts of the signal, such as random noise, or to extract useful parts of the signal, such as the components lying within a certain frequency range.The following block diagram illustrates the basic idea.There are two main kinds of filter, analog and digital. They are quite different in their physical makeup and in how they work. An analog filter uses analog electronic circuits made up from components such as resistors, capacitors and op amps to produce the required filtering effect. Such filter circuits are widely used in such applications as noise reduction, video signal enhancement, graphic equilibrium in hi-fi systems, and many other areas. There are well-established standard techniques for designing an analog filter circuit for a given requirement. At all stages, the signal being filtered is an electrical voltage or current which is the direct analogue of the physical quantity (e.g. a sound or video signal or transducer output) involved. A digital filter uses a digital processor to performnumerical calculations on sampled values of the signal. The processor may be a general-purpose computer such as a PC, or a specialized DSP (Digital Signal Processor) chip. The analog input signal must first be sampled and digitized using an ADC (analog to digital converter). The resulting binary numbers, representing successive sampled values of the input signal, are transferred to the processor, which carries out numerical calculations on them. These calculations typically involve multiplying the input values by constants and adding the products together. If necessary, the results of these calculations, which now represent sampled values of the filtered signal, are output through a DAC (digital to analog converter) to convert the signal back to analog form.Note that in a digital filter, the signal is represented by a sequence of numbers, rather than a voltage or current.The following diagram shows the basic setup of such a system.Unit refers to the input signals used to filter hardware or software. If the filter input, output signals are separated, they are bound to respond to the impact of the Unit is separated, such as digital filters filter definition. Digital filter function, which was to import sequences X transformation into export operations through a series Y.According to figures filter function 24-hour live response characteristics, digital filters can be divided into two, namely, unlimited long live long live the corresponding IIR filter and the limited response to FIR filters. IIR filters have theadvantage of the digital filter design can use simulation results, and simulation filter design of a large number of tables may facilitate simple. It is the shortcomings of the nonlinear phase; Linear phase if required, will use the entire network phase-correction. Image processing and transmission of data collection is required with linear phase filters identity. And FIR linear phase digital filter to achieve, but an arbitrary margin characteristics. Impact from the digital filter response of the units can be divided into two broad categories : the impact of the limited response (FIR) filters, and unlimited number of shocks to (IIR) digital filters.FIR filters can be strictly linear phase, but because the system FIR filter function extremity fixed at the original point, it can only use the higher number of bands to achieve their high selectivity for the same filter design indicators FIR filter called band than a few high-IIR 5-10 times, the cost is higher, Signal delay is also larger. But if the same linear phase, IIR filters must be network-wide calibration phase, the same section also increase the number of filters and net work complexity. FIR filters can be used the recursive method, not in a limited precision of a shock, and into the homes and quantitative factors of uncertainty arising from the impact of errors than IIR filter small number, and FIR filter can be used FFT algorithms, the computational speed. But unlike IIR filter can filter through the simulation results, there is no ready-made formula FIR filter must use computer-aided design software (such as MATLAB) to calculate. So, a broader application of FIR filters, and IIR filters are not very strict requirements on occasions.Unit from sub-functions can be divided into the following four categories :(1) Low-filter (LPF);(2) high-filter (HPF);(3) belt-filter (BPF);(4) to prevent filter (BSF).The following chart dotted line for the ideals of the filter frequency characteristics :2、MATLAB introducedMATLAB is a matrix laboratory (Matrix Laboratory) is intended. In addition to an excellent value calculation capability, it also provides professional symbols terms, word processing, visualization modeling, simulation and real-time control functions. MATLAB as the world's top mathematical software applications, with a strong engineering computing, algorithms research, engineering drawings, applications development, data analysis and dynamic simulation, and other functions, in aerospace, mechanical manufacturing and construction fields playing an increasingly important role. And the C language function rich, the use of flexibility, high-efficiency goals procedures. High language both advantages aswell as low level language features. Therefore, C language is the most widely used programming language. Although MATLAB is a complete, fully functional programming environment, but in some cases, data and procedures with the external environment of the world is very necessary and useful. Filter design using MATLAB, could be adjusted with the design requirements and filter characteristics of the parameters, visual simple, greatly reducing the workload for the filter design optimization.In the electricity system protection and secondary computer control, many signal processing and analysis are based on are certain types sinusoidal wave and the second harmonics of the system voltage and current signals (especially at D process), are mixed with a variety of complex components, the filter has been installed power system during the critical components. Current computer protection and the introduction of two digital signal processing software main filter. Digital filter design using traditional cumbersome formula, the need to change the parameters after recalculation, especially in high filters, filter design workload. Uses MATLAB signal processing boxes can achieve rapid and effective digital filter design and simulation.MATLAB is the basic unit of data matrix, with its directives expression mathematics, engineering, commonly used form is very similar, it is used to solve a problem than in MATLAB C, Fortran and other languages End precision much the same thing. The popular MATLAB 5.3/Simulink3.0 including hundreds of internal function with the main pack and 30 types of tool kits (Toolbox). kits can be divided into functional tool kits and disciplines toolkit. MATLAB tool kit used to expand the functional symbols terms, visualization modeling simulation, word processing and real-time control functions. professional disciplines toolkit is a stronger tool kits, tool kits control, signal processing tool kit, tool kits, etc. belonging to such communicationsMATLAB users to open widely welcomed. In addition to the internal function, all the packages MATLAB tool kits are readable document and the document could be amended, modified or users through original program the construction of new procedures to prepare themselves for kits.3、Digital filter designDigital filter design of the basic requirementsDigital filter design must go through three steps :(1) Identification of indicators : In the design of a filter, there must be some indicators. These indicators should be determined on the basis of the application. In many practical applications, digital filters are often used to achieve the frequency operation. Therefore, indicators in the form of general jurisdiction given frequency range and phase response. Margins key indicators given in two ways. The first is absolute indicators. It provides a function to respond to the demands of the general application of FIR filter design. The second indicator is the relative indicators. Its value in the form of answers to decibels. In engineering practice, the most popular of such indicators. For phase response indicators forms, usually in the hope that the system with a linear phase frequency bands human. Using linear phase filter design with the following response to the indicators strengths：①it only contains a few algorithms, no plural operations；②there is delay distortion, only a fixed amount of delay; ③the filter length N (number of bands for N-1), the volume calculation for N/2 magnitude.(2) Model approach : Once identified indicators can use a previous study of the basic principles and relationships, a filter model to be closer to the target system.(3) Achieved : the results of the above two filters, usually by differential equations, system function or pulse response to describe. According to this description of hardware or software used to achieve it.4、Introduction of DSPToday, DSP is widely used in the modern techno logy and it has been the key part of many products and played more and mo re important role in our daily life Recently, Northwestern Poly technical University Aviation Microelectronic Center has completed the design of digital signal processor co re NDSP25, which is aiming at TM S320C25 digital signal processor of Texas Instrument TM S320 series. By using top 2dow n design flow NDSP25 is compatible with instruction and interface timing of TM S320C25.Digital signal processors (DSP) is a fit for real-time digital signal processing for high-speed dedicated processors, the main variety used for real-time digital signal processing to achieve rapid algorithms. In today's digital age background, the DSP has become the communications, computer, and consumer electronics products, and other fields based device.Digital signal processors and digital signal processing is inseparably, we usually say "DSP" can also mean the digital signal processing (Digital Signal Processing), is that in this digital signal processors Lane. Digital signal processing is a cover many disciplines applied to many areas and disciplines, refers to the use of computers or specialized processing equipment, the signals in digital form for the collection, conversion, recovery, valuation, enhancement, compression, identification, processing, the signals are compliant form. Digital signal processors for digital signal processing devices, it is accompanied by a digital signal processing to produce. DSP development process is broadly divided into three phases : the 20th century to the 1970s theory that the 1980s and 1990s for the development of products. Before the emergence of the digital signal processing in the DSP can only rely on microprocessors (MPU) to complete. However, the advantage of lower high-speed real-time processing can not meet the requirements. Therefore, until the 1970s, a talent made based DSP theory and algorithms. With LSI technology development in 1982 was the first recipient of the world gave birth to the DSP chip. Years later, the second generation based on CMOS工艺DSP chips have emerged. The late 1980s, the advent of the third generation of DSP chips. DSP is the fastest-growing 1990s, there have been four successive five-generation and the generation DSP devices. After 20 years of development, the application of DSP products has been extended to people's learning, work and all aspects of life and gradually become electronics products determinants.中文翻译数字滤波器的仿真与实现随着信息时代和数字世界的到来，数字信号处理已成为当今一门极其重要的学科和技术领域。
IIR数字滤波器中英文对照外文翻译文献
(文档含英文原文和中文翻译)中英文资料对照外文翻译IIR Digital Filter DesignAn important step in the development of a digital filter is the determination of a realizable transfer function G(z) approximating the given frequency response specifications. If an IIR filter is desired,it is also necessary to ensure that G(z) is stable. The process of deriving the transfer function G(z) is called digital filter design. After G(z) has been obtained, the next step is to realize it in the form of a suitable filter structure. In chapter 8,we outlined a variety of basic structures for the realization of FIR and IIRtransfer functions. In this chapter,we consider the IIR digital filter design problem. The design of FIR digital filters is treated in chapter 10.First we review some of the issues associated with the filter design problem. A widely used approach to IIR filter design based on the conversion of a prototype analog transfer function to a digital transfer function is discussed next. Typical design examples are included to illustrate this approach. We then consider the transformation of one type of IIR filter transfer function into another type, which is achieved by replacing the complex variable z by a function of z. Four commonly used transformations are summarized. Finally we consider the computer-aided design of IIR digital filter. To this end, we restrict our discussion to the use of matlab in determining the transfer functions.9.1 preliminary considerationsThere are two major issues that need to be answered before one can develop the digital transfer function G(z). The first and foremost issue is the development of a reasonable filter frequency response specification from the requirements of the overall system in which the digital filter is to be employed. The second issue is to determine whether an FIR or IIR digital filter is to be designed. In the section ,we examine these two issues first . Next we review the basic analytical approach to the design of IIR digital filters and then consider the determination of the filter order that meets the prescribed specifications. We also discuss appropriate scaling of the transfer function.9.1.1 Digital Filter SpecificationsAs in the case of the analog filter,either the magnitude and/or the phase(delay) response is specified for the design of a digital filter for most applications. In some situations, the unit sample response or step response may be specified. In most practical applications, the problem of interest is the development of a realizable approximation to a given magnitude response specification. As indicated in section 4.6.3, the phase response of the designed filter can be corrected by cascading it with an allpass section. The designof allpass phase equalizers has received a fair amount of attention in the last few years. We restrict our attention in this chapter to the magnitude approximation problem only. We pointed out in section 4.4.1 that there are four basic types of filters,whose magnitude responses are shown in Figure 4.10. Since the impulse response corresponding to each of these is noncausal and of infinite length, these ideal filters are not realizable. One way of developing a realizable approximation to these filter would be to truncate the impulse response as indicated in Eq.(4.72) for a lowpass filter. The magnitude response of the FIR lowpass filter obtained by truncating the impulse response of the ideal lowpass filter does not have a sharp transition from passband to stopband but, rather, exhibits a gradual "roll-off."Thus, as in the case of the analog filter design problem outlined in section 5.4.1, the magnitude response specifications of a digital filter in the passband and in the stopband are given with some acceptable tolerances. In addition, a transition band is specified between the passband and the stopband to permit the magnitude to drop off smoothly. For example, the magnitude )(ωj e G of a lowpass filter may be given as shown in Figure7.1. As indicated in the figure, in the passband defined by 0p ωω≤≤, we require that the magnitude approximates unity with an error of p δ±,i.e.,p p j p for e G ωωδδω≤+≤≤-,1)(1.In the stopband, defined byπωω≤≤s ,we require that the magnitude approximateszero with an error of i s ,δ.e., ,)(s j e G δω≤ for πωω≤≤s .The frequencies p ω and s ω are , respectively, called the passband edge frequency and the stopband edge frequency. The limits of the tolerances in the passband and stopband,p δ and s δ, are usually called the peak ripple values. Note that the frequency response )(ωj e G of a digital filter is a periodic function of ω,and the magnitude response of a real-coefficient digital filter is an even function ofω. As a result, the digital filter specifications are given only for the range πω≤≤0.Digital filter specifications are often given in terms of the loss function,)(log 20)(10ωωζj e G -=, in dB. Here the peak passband ripple p α and theminimum stopband attenuation s α are given in dB,i.e., the loss specifications of a digital filter are given bydB p p )1(log 2010δα--=,dB s s )(log 2010δα-=. 9.1 Preliminary ConsiderationsAs in the case of an analog lowpass filter, the specifications for a digital lowpass filter may alternatively be given in terms of its magnitude response, as in Figure 7.2. Here the maximum value of the magnitude in the passband is assumed to be unity, and the maximum passband deviation, denoted as 1/21ε+,is given by the minimum value of the magnitude in the passband. The maximum stopband magnitude is denoted by 1/A.For the normalized specification, the maximum value of the gain function or the minimum value of the loss function is therefore 0 dB. The quantitymax α given bydB )1(log 20210max εα+= Is called the maximum passband attenuation. Forp δ<<1, as is typically the case, it can be shown thatp p αδα2)21(log 2010max ≅--≅The passband and stopband edge frequencies, in most applications, are specified in Hz, along with the sampling rate of the digital filter. Since all filter design techniques are developed in terms of normalized angular frequencies p ω and s ω,the sepcified critical frequencies need to be normalized before a specific filter design algorithm can be applied. Let T F denote the sampling frequency in Hz, and F P and F s denote, respectively,the passband and stopband edge frequencies in Hz. Then the normalized angular edge frequencies in radians are given byT F F F F p Tp T p p ππω22==Ω=T F F F F s Ts T s s ππω22==Ω= 9.1.2 Selection of the Filter Type The second issue of interest is the selection of the digital filter type,i.e.,whether an IIR or an FIR digital filter is to be employed. The objective of digital filter design is to develop a causal transfer function H(z) meeting the frequency response specifications. ForIIR digital filter design, the IIR transfer function is a real rational function of 1-z .H(z)=NMdNz z d z d d pMz z p z p p ------++++++++......2211022110 Moreover, H(z) must be a stable transfer function, and for reduced computational complexity, it must be of lowest order N. On the other hand, for FIR filter design, the FIRtransfer function is a polynomial in 1-z :∑=-=N n n zn h z H 0][)(For reduced computational complexity, the degree N of H(z) must be as small as possible. In addition, if a linear phase is desired, then the FIR filter coefficients must satisfy the constraint:][][N n h n h -±=T here are several advantages in using an FIR filter, since it can be designed withexact linear phase and the filter structure is always stable with quantized filter coefficients. However, in most cases, the order N FIR of an FIR filter is considerably higher than the order N IIR of an equivalent IIR filter meeting the same magnitude specifications. In general, the implementation of the FIR filter requires approximately N FIR multiplications per output sample, whereas the IIR filter requires 2N IIR+1 multiplications per output sample. In the former case, if the FIR filter is designed with a linear phase, then the number of multiplications per output sample reduces to approximately (N FIR+1)/2. Likewise, most IIR filter designs result in transfer functions with zeros on the unit circle,N with all of the zeros on the unit and the cascade realization of an IIR filter of orderIIRN+3)/2] multiplications per output sample. It has been shown that circle requires [(3IIRfor most practical filter specifications, the ratio N FIR/N IIR is typically of the order of tens or more and, as a result, the IIR filter usually is computationally more efficient[Rab75]. However ,if the group delay of the IIR filter is equalized by cascading it with an allpass equalizer, then the savings in computation may no longer be that significant [Rab75]. In many applications, the linearity of the phase response of the digital filter is not an issue,making the IIR filter preferable because of the lower computational requirements.9.1.3 Basic Approaches to Digital Filter DesignIn the case of IIR filter design, the most common practice is to convert the digital filter specifications into analog lowpass prototype filter specifications, and then to transform it into the desired digital filter transfer function G(z). This approach has been widely used for many reasons:(a) Analog approximation techniques are highly advanced.(b) They usually yield closed-form solutions.(c) Extensive tables are available for analog filter design.(d) Many applications require the digital simulation of analog filters.In the sequel, we denote an analog transfer function as)()()(s D s P s H a a a =, Where the subscript "a" specifically indicates the analog domain. The digital transfer function derived form H a (s) is denoted by)()()(z D z P z G = The basic idea behind the conversion of an analog prototype transfer function H a (s) into a digital IIR transfer function G(z) is to apply a mapping from the s-domain to the z-domain so that the essential properties of the analog frequency response are preserved. The implies that the mapping function should be such that(a) The imaginary(j Ω) axis in the s-plane be mapped onto the circle of the z-plane.(b) A stable analog transfer function be transformed into a stable digital transfer function.To this end,the most widely used transformation is the bilinear transformation described in Section 9.2.Unlike IIR digital filter design,the FIR filter design does not have any connection with the design of analog filters. The design of FIR filter design does not have any connection with the design of analog filters. The design of FIR filters is therefore based on a direct approximation of the specified magnitude response,with the often added requirement that the phase response be linear. As pointed out in Eq.(7.10), a causal FIR transfer function H(z) of length N+1 is a polynomial in z -1 of degree N. The corresponding frequency response is given by∑=-=N n n j j en h e H 0][)(ωω.It has been shown in Section 3.2.1 that any finite duration sequence x[n] of length N+1 is completely characterized by N+1 samples of its discrete-time Fourier transfer X(ωj e ). As a result, the design of an FIR filter of length N+1 may be accomplished by finding either the impulse response sequence {h[n]} or N+1 samples of its frequency response )H(e j ω. Also,to ensure a linear-phase design, the condition of Eq.(7.11) must be satisfied. Two direct approaches to the design of FIR filters are the windowed Fourier series approach and the frequency sampling approach. We describe the former approach in Section 7.6. The second approach is treated in Problem 7.6. In Section 7.7 we outline computer-based digital filter design methods.作者：Sanjit K.Mitra国籍：USA出处：Digital Signal Processing -A Computer-Based Approach 3eIIR数字滤波器的设计在一个数字滤波器发展的重要步骤是可实现的传递函数G（z）的接近给定的频率响应规格。
滤波器英语作文
滤波器英语作文Title: Understanding Filters: A Comprehensive Overview。
Filters are indispensable components in various fields, ranging from signal processing to image enhancement, and even in everyday appliances like air purifiers. These devices play a crucial role in isolating specific frequencies or elements from a broader spectrum, thereby refining or modifying the input in accordance with desired outcomes. In this essay, we delve into the fundamental principles, types, applications, and advancements in filter technology.Fundamental Principles:Filters operate based on fundamental principles ofsignal processing, manipulating input signals to achieve desired output characteristics. The core principle involves selectively allowing certain frequencies to pass through while attenuating others. This process is often describedin terms of frequency response, where filters exhibit varying degrees of attenuation or amplification across different frequency bands.Types of Filters:Filters can be broadly classified into analog and digital categories, each further divided into subtypes based on design and functionality.Analog Filters:1. Low-pass Filters: Permit frequencies below a certain cutoff while attenuating higher frequencies.2. High-pass Filters: Allow frequencies above a cutoff and attenuate lower frequencies.3. Band-pass Filters: Pass a specific range of frequencies while suppressing others.4. Band-stop Filters (Notch Filters): Suppress aspecific range of frequencies while passing others.5. All-pass Filters: Maintain the amplitude of all frequencies but introduce phase shifts.Digital Filters:1. Finite Impulse Response (FIR) Filters: Characterized by finite duration responses to impulse inputs.2. Infinite Impulse Response (IIR) Filters: Feature feedback, resulting in potentially infinite duration responses to impulse inputs.Applications of Filters:Filters find extensive applications across various domains, including:1. Signal Processing: Filtering noise from signals, separating desired signals from interference, and equalization.2. Image Processing: Enhancing image quality by removing noise, sharpening edges, or smoothing textures.3. Communication Systems: Filtering signals in modulation and demodulation processes, improving channel capacity and signal quality.4. Biomedical Engineering: Filtering biological signals for diagnostic purposes, such as electrocardiography (ECG) or electroencephalography (EEG).5. Audio Engineering: Equalization, noise reduction, and effects processing in audio production and playback systems.6. Control Systems: Filtering feedback signals to stabilize control loops and suppress oscillations.Advancements in Filter Technology:Recent advancements in filter technology have led toseveral innovations:1. Adaptive Filters: Capable of automatically adjusting filter parameters based on input characteristics, offering improved performance in dynamic environments.2. Multirate Filters: Exploit differences in sampling rates to achieve efficient signal processing, particularly in digital communications and multimedia applications.3. Sparse Filters: Utilize sparse signal representations to reduce computational complexity while maintaining filtering accuracy.4. Machine Learning-based Filters: Leveraging machine learning algorithms to adaptively learn filter characteristics from data, offering enhanced flexibility and performance.Conclusion:Filters serve as indispensable tools across a myriad ofapplications, enabling precise control over signal characteristics and facilitating numerous technological advancements. Understanding the principles, types, applications, and recent developments in filter technology is essential for engineers, researchers, and practitioners seeking to harness the full potential of these versatile devices. As technology continues to evolve, filters will undoubtedly remain integral components in shaping the future of various industries and disciplines.。
【精品】科技英语4低通滤波器原文和翻译
【关键字】精品Words and Expressionsintegrator n. 积分器amplitude n. 幅值slope n 斜率denominator n. 分母impedance n 阻抗inductor n. 电感capacitor n 电容cascade n. 串联passband n 通带ringing n. 振铃damping n. 阻尼，衰减conjugate adj. 共轭的stage v. 成为low-pass filters 低通滤波器building block 模块linear ramp 线性斜坡log/log coordinates 对数/对数坐标Bode plot 伯德图transfer function 传递函数complex-frequency variable 复变量complex frequency plane 复平面real component 实部frequency response 频率响应complex function 复变函数Laplace transform 拉普拉斯变换real part 实部imaginary part 虚部angular frequency 角频率frequency response 频率响应transient response 瞬态响应decaying-exponential response 衰减指数响应step function input 阶跃（函数）输入time constant 时间常数first-order filters 一阶滤波器second-order low-pass filters 二阶低通滤波器passive circuit 无源电路active circuit 有源电路characteristic frequency 特征频率quality factor n. 品质因子，品质因数circular path 圆弧路径complex conjugate pairs 共轭复数对switched-capacitor 开关电容negative-real half of the complex plane 复平面负半平面Unit 4 Low-pass FiltersFirst-Order FiltersAn integrator (Figure 2. la) is the simplest filter mathematically, and it forms the building block for most modern integrated filters. Consider what we know intuitively about an integrator. If you apply a DC signal at the input (i.e., zero frequency), the output will describe a linear ramp that grows in amplitude until limited by the power supplies. Ignoring that limitation, the response of an integrator at zero frequency is infinite, which means that it has a pole at zero frequency. (A pole exists at any frequency for which the transfer function's value becomes infinite.)（为什么为极点，为什么低通？）Figure A simple RC integratorWe also know that the integrator's gain diminishes with increasing frequency and that at high frequencies the output voltage becomes virtually zero. Gain is inversely proportional to frequency, so it has a slope of -1 when plotted on log/log coordinates (i.e., -20dB/decade on a Bode plot, Figure 2. 1b).Figure 2.1 b A Bode plot of a simple integratorYou can easily derive the transfer function asWhere s is the complex-frequency variable and is 1/RC. If we think of s as frequency, this formula confirms the intuitive feeling that gain is inversely proportional to frequency.The next most complex filter is the simple low-pass RC type (Figure 2. 2a). Its characteristic (transfer function) isWhen, the function reduces to , i.e., 1. When s tends to infinity, the function tends to zero, so this is a low-pass filter. When, the denominator is zero and the function's value is infinite, indicating a pole in the complex frequency plane. The magnitude of the transfer function is plotted against s in Figure 2. 2b, where the real component of s () is toward us and the positive imaginary part () is toward the right. The pole at - is evident. Amplitude is shown logarithmically to emphasize the function's form. For both the integrator and the RC low-pass filter, frequency response tends to zero at infinite frequency; that is, there is a zero at. This single zero surrounds the complex plane.But how does the complex function in s relate to the circuit's response to actual frequencies? When analyzing the response of a circuit to AC signals, we use the expression for impedance of an inductor and for that of a capacitor. When analyzing transient response using Laplace transforms, we use sL and 1/sC for the impedance of these elements. The similarity is apparent immediately. The in AC analysis is in fact the imaginary part of s, which, as mentioned earlier, is composed of a real part and an imaginary part.If we replace s by in any equation so far, we have the circuit's response to an angular frequency. In the complex plot in Figure 2.2b, and hence along the positive j axis. Thus, the function's value along this axis is the frequency response of the filter. We have sliced the function along the axis and emphasized the RC low-pass filter's frequency-response curve by adding a heavy line for function values along the positive j axis. The more familiar Bode plot (Figure 2.2c) looks different in form only because the frequency isexpressed logarithmically.（根据图翻译这两句话）Figure 2.2a A simple RC low-pass filterWhile the complex frequency's imaginary part () helps describe a response to AC signals, the real part() helps describe a circuit's transient response. Looking at Figure 2.2b, we can therefore say something about the RC low-pass filter's response as compared to that of the integrator. The low-pass filter's transient response is more stable, because its pole is in the negative-real half of the complex plane. That is, the low-pass filter makes a decaying-exponential response to a step-function input; the integrator makes an infinite response. For the low-pass filter, pole positions further down the axis mean a higher, a shorter time constant, and therefore a quicker transient response. Conversely, a pole closer to the j axis causes a longer transient response.So far, we have related the mathematical transfer functions of some simple circuits to their associated poles and zeroes in the complex-frequency plane . From these functions, we have derived the circuit ’s frequency response (and hence its Bode plot) and also its transient response. Because both the integrator and the RC filter have only one s in the denominator of their transfer functions, they each have only one pole. That is, they are first-order filters .Figure 2.2b The complex function of an RC low-pass filterFigure 2.2c A Bode plot of a low-pass filterHowever, as we can see from Figure 2.1b, the first-order filter does not provide a very selective frequency response. To tailor a filter more closely to our needs , we must move on to higher orders. From now on, we will describe the transfer function using f(s) rather than the cumbersome IN OUT V V . Second-Order Low-Pass FiltersA second-order filter has 2s in the denominator and two poles in the complex plane. You can obtain such a response by using inductance and capacitance in a passive circuit or by creating an active circuit of resistors, capacitors, and amplifiers. Consider the passive LC filter in Figure 2.3a, for instance. We can show that its transfer function has the formand if we defineLC /120=ωand R L Q /0ω=,then where 0ωis the filter's characteristic frequency and Q is the quality factor (lower R means higher Q).Figure 2.3a An RLC low-pass filterThe poles occur at s values for which the denominator becomes zero; that is,when 0/2002=++ωωQ s s . We can solve this equation by remembering that the roots of 02=++c bx ax are given byIn this case, a = 1, b 0ω=, and 20ω=c .The term (ac b 42-) equals ()4/1220-Q ω, so if Q isless than 0.5 then both roots are real and lie on the negative-real axis. The circuit's behavior is much like that of two first order RC filters in cascade . This case isn't very interesting, so we'll consider only the case where Q > 0.5, which means ()ac b 42-is negative and the roots are complex.Figure 2.3b A pole-zero diagram of an RLC low-pass filterThe real part is therefore a b 2/-, which is Q 2/0ω-, and common to both roots. The roots' imaginary parts will be equal and opposite in signs. Calculating the position of the roots in the complex plane, we find that they lie at a distance of0ωfrom the origin, as shown in Figure 2.3b. Varying 0ω, changes the poles' distance from the origin. Decreasing the Q moves the poles toward each other, whereas increasing the Q moves the poles in a semicircle away from each other and toward the ωj axis. When Q = 0.5, the poles meet at 0ω-on the negative-real axis. In this case, the corresponding circuit is equivalent to two cascaded first-order filters.Now let's examine the second-order function's frequency response and see how it varies with Q. As before, Figure 2.4a shows the function as a curved surface, depicted in the three-dimensional space formed by the complex plane and a vertical magnitude vector . Q =0.707, and you can see immediately that the response is a low-pass filter.The effect of increasing the Q is to move the poles in a circular path toward the ωj axis. Figure2.4b shows the case where Q = 2. Because the poles are closer to the ωj axis, they have a greater effect on the frequency response, causing a peak at the high end of the passband .Figure 2.4a The complex function of a second-order low-pass filter (Q = 0.707)Figure 2.4b The complex function of a second-order low-pass filter (Q = 2)There is also an effect on the filter's transient response. Because the poles' negative-real part is smaller, an input step function will cause ringing at the filter output. Lower values of Q result in less ringing, because the damping is greater. On the other hand, if Q becomes infinite, the poles reach the ωj axis, causing an infinite frequency response (instability and continuous oscillation) at 0ωω=. In the LCR circuit in Figure 2.3a, this condition would be impossible unless R=0. For filters that contain amplifiers, however, the condition is possible and must be considered in the design process.A second-order filter provides the variables 0ωand Q, which allow us to place poles wherever we want in the complex plane. These poles must, however, occur as complex conjugate pairs , in which the real parts are equal and the imaginary parts have opposite signs. This flexibility in pole placement is a powerful tool and one that makes the second-order stage a useful component in many switched-capacitor filters. As in the first-order case, the second-order low-pass transfer function tends to zero as frequency tends to infinity. The second-order function decreases twice as fast, however, because of the 2s factor in the denominator. The result is a double zero （零点） at infinity. 低通滤波器一阶滤波器从数学公式上讲，积分器（见图2.1a ）是最简单的滤波器；它是构成大多数现代滤波器的基本模块。
滤波器 外文翻译 外文文献 英文文献 用改进的窗函数设计FIR数字滤波器
Research on FIR Digital Filter Design Using an Improved Window FunctionTAN Jiajie , LUO Changyou, HUANG Sanwei ，DENG Xiaohui( Department of Physics and Electronic Information Science, Hengyang Normal University, Hengyang Hunan 421008, China)Abstract : Window function has been used to design a linear phase digital filer for long times, but the use o f optimization techniques for designing digital filter has become widespread in recent year A new met ho d has been proposed to improve FIR window function in this paper ，T he window function that combines with co sine sequences in linear is different from previous Hann ,Hamming and Blackman window function The paper also proposes linear programming to optimize characterization of FIR digital filter according to its magnitude condition, and gives out t he algorithm to design dig ital filter using the improved window function ,Finally , we have designed FIR filter using new window for simulation and compared w it h the filter designed by Hamming window, Blackman window function T he simulation results show that filters designed using this method to meet t he design specificationsKey words: improved window function; FIR digital filter ; window function; linear programming0 lead speechThe design method of FIR digital filters are mainly: window function method, frequency sampling method and the chebyshev etc corrugated approximation method [1-4]. Window function method is the most commonly used designing FIR digital filters, the simplest method of [4-5]. The essence of window function method is the truncated ideal impulse response to approximate the method petitions filter index. Frequency sampling method is a design optimization method for its shortcoming is when the design that use the variable is limited to a few samples values of transitional, cut-off frequency not easy control [3]. Chebyshev etc corrugated approximation method is a kind of optimization design, but existing computational complexity, big disadvantage computation [1-2].Window function method is simple in design, have closed form of formula, thus very practical. Defect is the stopband bandpass, cut-off frequency not easy control [2-3]. Digital filter, window function of auto-heating window function method of selecting, the key is: design to choose the appropriate window function, choose the right order number of digital filter, improve amplitude frequency characteristics, reduce Gibbs phenomenon, solve convergence problem [1-2]. [3] choose window function, through to Guass Guass window function improved, design a low-pass filter has better superiority; [4] the error information, using the known in the iteration process through the window function method continuously revised design result in filter order number, under the condition of invariable frequency response approximation, filter ideal frequency response. [5] use integer sequence, such as where Fibonacci sequence, Golomb sequence, ConwayHofstadter Recursive sequence, Triangular series produce window function to design the filter, its effect is better than that of classical design method. [6] choose dual window window function sequence of structure was system characteristics approximation error is the minimum; [7] will be well Saramaki Dolph - and Chebysheve window with the well designed, its effect FIR digital filters than Kaiser well; [8] put good effect in Hamming ReImann well well well and Kaiser window. [9] put forward a kind of exponential window function, this window function has the width can be adjusted with the window design characteristics, the digital filters have more centralized, Lord disc energy side-lobe less features. [10] using linear programming design linear phase fir filter ascending cosine to 100 % super bandwidth. [11] linear programming method is adopted to design digital filter. This paper USES the existing window function, and carry on the weighted combination, reference [10 or 11], and linear programming with long Hamming, Blackman window are compared. The advantages of this method is strong logicality, goal clear, easy to achieve, and to explore the best solutions.1 common window functionWindow function select principle: window function as focus on energy, Lord disc transitional steep; Reduce the window function spectrum side-lobe level, increase stopband attenuation, and reduce the stopband bandpass and ripple effect. Common window function have [1-4] : Rectangle window, Hanning window, Hamming window, Blackman window, Kaiser window. Window function method design idea of FIR filters is [1-2] : make sure the frequency response of ideal filter )(ωj d e H .The frequency response of practical design filter ∑-=-=10)()(N n j j e n h e H ωωTo approximate )(ωj d e H .For again ∑-=-=10)()(N n j j e n h e H ωωReverse transform get Finally use window function )(n w To truncate )(n h d ,mean h( n) =)(n h d )(n w .To truncate )(n h d ,Will produce gibbs phenomenon, all the window function choices to reduce this phenomenon for the purpose. Judge ideal window function mainly according to the following three criteria! The Lord is high double amplitude and its width should try to narrowThe amplitude side-lobe fast speed, the biggest drop side-lobe relative to the main valve should be as low as possible. #transitional requirements will try to narrow. Facts prove the two standard cannot simultaneously satisfy window function should be, so the twocompromise [1-3]. In order to reduce caused due to add window truncation ripple and transitional grows wider impact in engineering design common Hamming window and Kaiser window.2 improved window function [1-2] enumerated window function, Hanning window, Hamming window, Blackman window is cosine sequence andrectangular sequence of linear combination. In order to restrain the amplitude,side-lobe Hanning window, Hamming window on the basis of the second, add cosine, when the harmonic component design and ideal window function and related to the frequency response of different from Blackman window, window function improved form below )(14cos 12cos )(n N R N n c N n b a n ⎥⎦⎤⎢⎣⎡-+-+=ππω (1)Formula (1) of a, b, c undetermined, their size and given filter technology indexes related. For convenience, this window function length choice for odd. The next several special case discussion this type. Case 1, take a = 1, b = c = 0, for rectangular window. Condition 2, take a = 0.5, b = - 0.5, c = 0, for Hann window. Case 3, take a = 0.53, b = - 0.46, c = 0, for Hamming window.Situation, a = 4, b = 0 0.42 j c = 0.08, 5, Blackman window for. By aboveknowable, the improved window function with these four window function the nature, belong to the general form of the window function.3 improved window function algorithmAccording to the given filter technology index )(ωj d e H ,Determine the backlog filter unit, but by sampling response formula below ask out:ωπωππωd e e H n h j j d d ⎰-=)(21)( (2)Calculating the actual filter unit sampling response:h( n) = )(n h d )(n w (3)Filter the frequency response is:∑-=-=10)()(N n j j e n h e H ωω（4） Will formula (1) generation into the formula (4) :ξωππjn N n n d j e N n c N n b a h e H --=⎥⎦⎤⎢⎣⎡-+-+=∑14cos 12cos )(10)( (5) Reference [1-2] [10 or 11], consider FIR filters satisfy the first kind of linearphase conditions, For 21-N Accidentally symmetry, And N an odd number,ordering h ( n) = )(n h d ⨯⎥⎦⎤⎢⎣⎡-+-+14cos 12cos N n c N n b a ππ。