数字滤波器的外文翻译
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。
signal.butter 滤波器的计算的公式
信号滤波是数字信号处理领域中的重要内容，它可以有效地消除噪音和干扰，提高信号的质量和可靠性。
而 signal.butter 滤波器作为一种常用的数字滤波器，在实际应用中具有广泛的使用价值。
本文将从signal.butter 滤波器的计算公式入手，深入探讨其原理、应用和优缺点，以帮助读者更好地理解和应用这一主题。
一、signal.butter 滤波器的计算公式signal.butter 函数是 Python 中 scipy.signal 模块中的一个函数，用于设计数字 Butterworth 滤波器。
它的计算公式如下：```pythonb, a = signal.butter(N, Wn, btype='low', analog=False,output='ba', fs=None)```其中，参数含义如下：- N：滤波器的阶数，代表滤波器的复杂度，对应于滤波器的极点个数。
- Wn：归一化的截止频率，取值范围为 0 < Wn < 1，对于数字滤波器而言，截止频率 Wn 实际上代表了模拟滤波器的截止频率除以采样频率的一半。
- btype：滤波器的类型，可选值为 'low'、'high'、'bandpass'、'bandstop'，分别代表低通、高通、带通和带阻滤波器。
- analog：是否为模拟滤波器，如果为 True，则设计模拟滤波器；如果为 False，则设计数字滤波器。
- output：输出类型，可选值为 'ba'、'zpk'、'sos'，分别代表输出传递函数系数、零极点、二阶级联滤波器表示。
- fs：采样频率，用于指定数字滤波器的采样频率。
根据以上计算公式，我们可以灵活设置滤波器的阶数、截止频率、类型等参数，根据实际需求来设计滤波器，以实现对信号的滤波处理。
数字滤波器概念及设计
数字滤波器概念及设计数字滤波器概念及设计•数字滤波器分类•滤波器相关函数•常见滤波器•o平均滤波器o平滑滤波器o限幅滤波器o中值滤波器数字滤波器(digital filter)是一个离散时间系统，通常按照预定的算法，将输入的离散时间信号或数字信号转化为所要求的离散时间或数值信号，相对于模拟滤波器而言，数字滤波器具有精度高、可靠性高、灵活性好、可程序控制调试的优点。
数字滤波器分类滤波器可以分为经典滤波器和现代滤波器两类经典滤波器：经典滤波器（classical filter),其原理是假定期望信号和噪声各占不同频段，滤波后去除噪声频段的信号，保留期望频段的信号。
•按频率分类：•(1)低通滤波器：low-pass filter•(2)高通滤波器：high-pass filter•(3)带通滤波器：band-pass filter•(4)带阻滤波器：band-stop filter•(5)全通滤波器：all-pass filter•按单位冲击响应特性分类：•(1)无限冲击响应滤波器:infinite impulse respance•(2)有限冲击响应滤波器：finite impulse respance•其中有限冲击响应滤波器可以参考FIR数字滤波器,该文介绍了有限冲击响应滤波器的设计方法，和代码实现。
•现代滤波器：•现代滤波器又称为统计最优滤波器(statistical optimal filter),与经典滤波器不同，统计最优滤波器是依据某些统计最优规则，从带噪声的测试信号中对由用信号或信号参数进行估计。
•（1）维纳滤波器：Wiener filter•（2）卡尔曼滤波器：Kalman filter•（3）自适应滤波器：adaptive filter•现代滤波器中，卡尔曼滤波器比较常见，其公式推导和实现方法可以参考卡尔曼滤波原理介绍及算法实现,该文介绍了详细的推导公式和代码实现。
滤波器相关函数当ak全为0时，滤波器称为有限冲击响应滤波器，当不全为0时，称为无限冲击响应滤波器。
信号分析与处理英语单词
1.滤波器（filter）2.信号(signal)3.信息（information）4.函数（function）5.消息（message）6.知识（knowledge）7.频率(frequency)8.幅度(amplitude)9.相位(phase)10.模拟信号(analog signal)11.量化信号(quantized signal)12.抽样信号(sampling signal)13.数字信号(digital signal)14.确定性信号(determinate)15.随机信号(random)16.周期信号(periodic)17.非周期信号(nonperiodic)18.时限信号(time finite)19.频限信号(frequency finite)20.频谱分析(frequency spectrum)21.时域(Time domain)22.频域(Frequency domain)23.指数信号(exponential)24.复指数函数(complex exponential)25.欧拉公式(Euler's formula)26.阶跃(step)27.符号(signum)28.单位冲激(unit impulse)29.移位（shift）30.反褶（reverse）31.尺度倍乘(scaling)32.微分(differential)33.积分(integration)34.定积分(definite integration)35.奇与偶(odd & even)36.线形系统（Linear System）37.实部与虚部(real & imaginary)38.正交(orthogonal)39.谐波(harmonic)40.卷积(convolution)41.齐次性（homogeneity）42.叠加性（additivity）43.矢量（vector）44.三角函数（trigonometric function）45.完备(perfect)46.傅里叶级数（Fourier series）。
数字滤波器的截止频率
数字滤波器的截止频率数字滤波器（Digital Filters）是数字信号处理中非常重要的一个概念，它可以对数字信号进行去噪、衰减特定频率分量等处理。
数字滤波器有很多种类型，如FIR （Finite Impulse Response）滤波器、IIR（Infinite Impulse Response）滤波器、Butterworth滤波器等。
其中，数字滤波器的截止频率是非常重要的参数，下文将详细介绍数字滤波器的截止频率和相关概念。
一、数字滤波器的概念和分类数字滤波器是数字信号处理中用于对数字信号进行滤波处理的一种算法。
数字信号处理是一种利用数字电路或计算机对信号进行数字化处理的技术。
数字滤波器可以分为两大类：有限长冲激响应（FIR）滤波器和无限长冲激响应（IIR）滤波器。
FIR滤波器是由有限长的冲激响应组成的数字滤波器，其特点是具有线性相位，所以能够保持信号的波形特征。
IIR滤波器由无限长的冲激响应组成，具有递归结构，其特点是能够实现高阶滤波器的设计，但在设计过程中需要关注其稳定性和相位响应特性。
二、数字滤波器的截止频率数字滤波器的截止频率又称为截止频带，是指滤波器对于输入信号的某一频率分量进行截止（即衰减）的频率。
截止频率的选择是数字滤波器设计中非常重要的一环，直接关系到滤波器的性能。
截止频率是由滤波器的截止频带宽和截止频率位置两个参数决定的。
例如，一个FIR低通滤波器，其截止频率为500 Hz，截止频带宽为100 Hz，则其在0-400 Hz的带内不做滤波，而在500-2500 Hz的带外进行完全滤波。
在数字滤波器设计中，有几种不同的表示方式可以用来描述截止频率，分别如下：1. 离散时间模拟滤波器（DTAF）的截止频率DTAF滤波器是一种与线性时不变系统等效的差分方程，其截止频率以nyquist为单位表示，即采样频率的一半。
例如，若采样频率为2 kHz，则DTAF滤波器的截止频率为1 kHz。
数字信号处理(DSP)专业词汇
系统：system 信号：signal模拟信号：analog signal 数字信号：digital signal模/数转换：analog-to-digital conversion 频谱：spectrum数字滤波：digital filtering 滤波器：filter采样：sample 保持：hold数字代码：digital code 量化电平：quantization level时域：time domain 频域：frequency domain低频：low frequency 高频：high frequency低通滤波器：low pass filter 高通滤波器：high pass filter带通滤波器：band pass filter 带阻滤波器：band stop filter零阶保持信号:zero order hold signal 平滑：smooth采样周期：sampling period 频率分量:frequency elements图像处理：image processing 传感器：sensor电压：voltage 电流：current•anti-aliasing filter 抗混叠滤波器•anti-imaging filter 抗镜像滤波器•sampling interval 采样间隔•=sampling period 采样周期•sampling frequency 采样频率•=sampling rate 采样速率•sampling theorem 采样定理•Nyquist sampling rate 奈奎斯特采样率•Nyquist frequency 奈奎斯特频率•Nyquist range 奈奎斯特范围•oversampling 过采样undersampling 欠采样•quantization step 量化步长quantization noise量化噪声•bit rate 比特率•数字函数：digital function 合成函数：composite function •二维数字信号：two-dimensional digital signal•语音信号：speech signal 量化方案：quantization scheme •脉冲函数：impulse function 单位脉冲函数：unit impulse function •阶跃函数：step function 幂函数:power function •指数函数: exponential function 正弦函数：sine function•余弦函数：cosine function 复平面：complex plain•欧拉恒等式：Euler’s identity 模拟频率：analog frequency •数字频率:digital frequency 采样间隔：sampling interval •相移：phase shift 像素：pixel•灰度级：gray scale•roll-off 滚降gain 增益•pass band 通带stop band 阻带•bandwidth 带宽linear system 线性系统•superposition 叠加原理time-invariant 时不变•causal system因果系统difference equation差分方程•filter coefficient滤波器系数recursive filter 递归滤波器•nonrecursive filter 非递归滤波器finite word length effect有限字长效应•impulse response 脉冲响应infinite impulse response （IIR)无限脉冲响应•finite impulse response (FIR)有限脉冲响应•moving average filter 滑动平均滤波器•step response 阶跃响应•z transform z变换•region of convergence 收敛域•inverse z transform 逆z变换•transfer function 传输函数•partial fraction expansion 部分分式展开•cover-up method 覆盖法•zero 零点pole 极点•marginally stable 临界稳定unstable 不稳定•傅立叶变换：Fourier Transform•滤波器形状：filter shape•频率响应:frequency response•频率特性：frequency characteristics•离散时间傅立叶变换：Discrete Time Fourier Transform•幅度响应：magnitude response•相位响应：phase response•传输函数：transfer function•相位差：phase difference•采样频率：sampling frequency•white noise 白噪声•magnitude spectrum 幅度频谱•phase spectrum 相位频谱•discrete Fourier series（DFS)离散傅里叶级数•有限脉冲响应滤波器：finite impulse response filter•无限脉冲响应滤波器：infinite impulse response filter•相位失真：phase distortion•理想低通滤波器：idle low pass filter•窗函数：window function 稳定性：stability•通带波纹：pass band ripple•阻带波纹：stop band ripple•通带边缘频率:pass band edge frequency•过渡带宽度：transition width•矩形窗：Rectangular Window•汉宁窗：Hanning Window•哈明窗:Hamming Window•布莱克曼窗:Blackman Window•凯塞窗:Kaiser Window•项数:number of terms 衰减:attenuation•增益:gain•采样频率:sampling frequency•infinite impulse response filter(IIR)无限脉冲响应滤波器•bilinear transformation 双线性变换•prewarping equation 预扭曲方程•Butterworth filter 巴特沃斯滤波器•Chebyshev Type I filter 切比雪夫I 型滤波器•Chebyshev Type II filter 切比雪夫II 型滤波器•elliptic filter 椭圆滤波器•Impulse invariance method 脉冲响应不变法•discrete Fourier transform (DFT) 离散傅里叶变换•inverse DFT 逆离散傅里叶变换•phase spectrum 相位频谱•frequency spacing频率间隔•resolution分辨率•smear模糊•spectral leakage 频谱泄漏•spectrogram频谱图•fast Fourier transform (FFT) 快速傅里叶变换•butterfly 蝶形。
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。
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FIR 数字滤波器的有限字长系数优化的比较研究
拜彻尔，泰勒，罗兰
威尔士大学纽波特学院运算工程学校
摘要：实时数字滤波器频率响应的精度受实现时系数约束条件即有限字长(FWL)的影响。
该文仅考虑FIR 数字滤波器有关的FWL 问题。
准确和近似响应之间的最大误差限的约束条件所对应的理论问题和统计误差值都进行了详细的研究。
利用实数值遗传算法作为优化工具，并由若干设计案例的FWL 效应获得其最大误差限和误差值。
由此，完成了简单凑整逼近、遗传算法优化、整数规划法，以及简单希尔登山者方法之间的比较。
关键词：实时数字滤波器； 有限字长；遗传算法；整数规划
1. 前言
FIR 数字滤波器广泛用于图像处理、移动通信、医疗电子，以及很多其他的信号处理应用。
为降低能耗和提高运算量，截断系数到最短长度是有优势的。
然而，该截断会引起滤波嚣设计参数的变化，在某些情况下这是不可接收的。
此即优化问题，即尽可能地选择近似系数值的微小变化量，以便最好的服从设计规范标准。
针对有限脉冲响应(FIR)滤波器形式结构的线性相位已被证明是鲁棒的，因而FWL 系数的自我实现的研究是极具有吸引力的[1]。
FWL FIR 对称数字滤波器的研究涉及到一组系数的选择，从而这个新频率响应可以作为无限准确系数截断的一个结果，可以最大的接近所给定的规范频率响应。
已知的为解决该问题所使用的算法均基于两种方法：局部搜索法[2]和整数规划分支界限法[3,4]。
局部搜索法需要选择一组可行的FWL 系数(称为四舍五入值)，用以给出一个频率响应并用以检验H 的领域。
同时要选定滤波器的传递函数，以便得到更好的滤波器H'，即具有低误差函数的滤波器。
如果找到了这样的一个滤波器H'，那么便可用H'来代替H ，而算法即可进入下一步或者终止。
分支界限算法涉及对一组可能解所构成的树的系统性修正，这些解依赖于由枚举总数所确定的下界值。
这两种算法本质上计算密集，且不能保证全局优化。
其问题即是在于进一步复合，使其更加灵敏以便增加滤波器长度。
2. FWL 系数及误差目标函数
用以导出FWL 系数的最常用定点算法是直接量化法。
使用标准滤波器设计技术导出的高精度系数在该方法中首次被利用，以得出FWL 的量化系数。
如下量化系数的起始解给出。
h ri =round[h ei 2B-1] i=0,1,2,...,N-1 (1)
这里，h ri 为四舍五入系数，hei 为高精度系数，B 为用以描述系数的位数，N 为滤波器长度。
优化过程的主要目的在于极小化目标函数，其明确目标为获得一个与期望的响应尽可能接近的滤波器频率响应。
目标函数被用于500个等距频率的格点。
目标函数通过以下式来评价：
}H max ,H 110max{max }H H 1{ObjV s p s s p p i i L
s
i 2
i P
i 2
i -++-=∑∑== (2)
H ip =遗传算法优化滤波器在通带中对应频率的幅值响应
H is =遗传算法优化滤波器在阻带中对应频率的幅值响应 L=频率格点的数目（500）
P=通带的截止频率数 S=阻带的截止频率数
(2)式所表述的平方偏差和加权最大偏差和的综合即可获得优良的整体频率响应。
当优化目标函数仅使用最大化偏差时，这些响应不受初期试验中观察到的相位差的影响，。
3. FIR 滤波器的频带选择的遗传算法的优化
在这一部分我们认为波带选择的问题是为了使理想响应被指定在被选到的通带或阻带以上。
理想函数D(ω)包含大量的脱节带频，而K=1,……，对于于每一个K ，D(ω)是用于结晶所有的ωk Ω∈。
如果有着无限精度小数的滤波器是H(ω)同时使用FWL 系数近似滤波器是H'(ω)，那最大误差界是由
为了进行比较研究，托代克和史代比所使用的10个滤波器例子用于系数优化，基于整数规划的方法也用于此处。
这10个滤波器被分成四组，如表1所示：
滤波器规范组
表2表明对于所有 理想响应的最大化误差的结果，表2所使用的界值是通过使用等式3而得来的。
整数规划方法的比较清楚地表明了关于遗传算法优化滤波器的一个明显提高，它也表明等式3的界值是与使用遗传算法优化滤波器而得到的最大化误差相一致。
遗传算法优化滤波器已生成了略低的最大化误差值，同20%滤波器的界值比较，即A25/5和C15/5滤波器。
另一方面，相比较于20%的滤波器的界值整数规划滤波器有更好的表现。
B25/7滤波器的一个响应例子由图1表示。
它表明如期望所示尽管圆润的响应伴随着准确的响应，遗传算法优化响应伴随着理想响应的要求即是滤波器B25/7通带里的1,。
图1展示了一个有关滤波器B25的最大化误差大小与字节数的比较。
表1.(a)简单圆的响应大小，对于滤波器B25/7遗传算法优化和整数规化优化系数，(b)对于B25滤波器误差大小和字节数的比较。
4.简单的登山科技和详细搜索
为了检验遗传算法优化结果的强健性和准确度，简单攀山算法的计算方法，例如最陡爬坡和最近爬坡被用于选择如表1所示的滤波器，为了遗传算法优化所用的搜索空间进行了随机样本测试。
另外，对于以少部分低阶滤波器，进行了一个超越相匹配的搜索空间的详细的搜索。
这个搜索所用攀山算法是基于用于二进制字符串的并且根据FIR 滤波器的整值的号码进行了改编。
开头的一个整值的号码系数集是由随机扰动的四舍五入系数通过加1或减1， 如图2
简单的攀山算法的流程图
SAHC：最陡爬坡
NAHC：最近爬坡
表示四舍五入系数值的搜索空间加1或减1
最陡爬坡和最近爬坡，也为了选择滤波器而进行的随机样本和详细搜索的结果如表3所示。
结果表明有星号的代表那些比加1或减1偏离更厉害的四舍五入的系数值。
数据同时也表明了详细搜索仅限于对四舍五入系数进行加1或减1。
证据表明遗传算法优化可以连续产生好的结果（见表2）。
尽管最陡爬坡的攀山技术对于选定数量的滤波器也表现出非凡的好结果。
5.结论
在这篇文章中，我们探索了FIR数字滤波器有限字长的遗传算法优化的问题。
大量的频段选择滤波器的遗传算法优化是考虑在内的。
对于这样的滤波器，
基于整数规划方法的优化结果和简单攀山技术的结果进行了比较。
对大部分所选的滤波器，遗传算法优化在此表现出了连续的改善。
简单攀山技术（特别是最陡爬坡）所用的优化方法通过产生好的结果已经变现出很好的潜力，通常这在所考虑范围内的滤波器是不符合要求的，然而遗传算法技术已经显示了一个强健的，实用的，和高效率的优化工具。
另外，它就像是遗传算法代码以600兆赫兹的速度奔腾与电脑上伴随第二部分所给的参数，超过了完整的优化方法，每个滤波器接近以30秒的速度在优化。
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