TWO-DIMENSIONAL FOURIER TRANSFORM ANALYSIS OF HELICOPTER FLYOVER NOISE
Coherent Two-Dimensional Fourier Transform Infrared
Coherent Two-Dimensional Fourier Transform InfraredSpectroscopyM.Khalil,N.Demirdöven and A.TokmakoffDepartment of Chemistry,Massachusetts Institute of Technology,Cambridge,MA02139Telephone:(617)-253-4503,Fax:(617)-253-7030,E-mail:tokmakof@Abstract:Purely absorptive two-dimensional(2D)infrared vibrational spectra are obtained byadding together rephasing and non-rephasing2D spectra.The modulation of cross-peaks andemergence of new peaks are demonstrated as a function of the mixing period.2000Optical Society of AmericaOCIS codes:(300.6340)Spectroscopy,infrared;(300.6530)Spectroscopy,ultrafastTwo-dimensional(2D)infrared(IR)vibrational spectroscopy has recently been employed to study the structure and correlated dynamics of strongly coupled C≡O vibrations in metal dicarbonyl compounds and to determine the structure of small peptides in solution[1-5].Femtosecond heterodyne-detected third-order mid-infrared responses obtained as a function of an initial preparation period and a final detection period are Fourier transformed to give a 2D IR rmation on transient and evolving molecular structures is encoded in the position,amplitude, and shape of cross peaks in the2D IR spectrum.From a practical perspective,the use of this method requires the ability to obtain intuitive and physically relevant spectra with purely absorptive lineshapes.This study demonstrates the technique of2D Fourier transform(FT)IR spectroscopy using two different third-order non-linear signals to obtain purely absorptive features in the2D vibrational spectrum of the carbonyl stretches of dicarbonylacetylacetonato rhodium(I)(RDC)dissolved in hexane.The method is then used to explore the effects of relaxation on the various features in the2D vibrational spectra by introducing a variable mixing period.2D FT IR spectroscopy uses three field-matter interactions with the three input fields E a(k a),E b(k b)and E c(k c) arranged in a box-car geometry to generate a third-order non-linear polarization in the phase-matched directionk s=−k a+k b+k c.Two different signals are obtained at k s which differ only in the time ordering of the k a and k b pulses:S I=−k1+k2+k3(rephasing)and S II=+k1−k2+k3(non-rephasing).This technique is experimentally realized using a five-beam IR interferometer with90fs pulses centered at4.9µm.The incoming IR beam is split into4equal parts,three of which are used as input beams while the fourth beam is further split into a tracer and a local oscillator(LO).The tracer beam is sent along the path of the signal and is blocked during data collection. After the sample,the signal beam is spatially and temporally overlapped with the LO and dispersed in a monochrometer onto a64channel MCT detector.Rephasing and non-rephasing heterodyned signals are collected as a function ofτ1(delay between the first two pulses)for a particular mixing period,τ2(delay between the second and third pulses)by moving retroreflectors mounted on stepper-controlled translation stages.To determine the timing between pulses a and b to withinλ/10,the pulses are recombined after the sample and dispersed in a second monochrometer.Interference fringes collected as the timing between the two pulses is varied are used to calibrate theτ1axis.Fourier transforming along the correctedτ1axis leads to symmetric features in the resulting2D spectra.It is known from NMR,that collecting only the rephasing or the non-rephasing signals yields lineshapes that have mixed-phase character resulting in both absorptive and dispersive features in the real part of the2D spectrum. Pure absorptive lineshapes can be obtained by adding together the rephasing and non-rephasing2D spectra.Figure 1shows the rephasing and non-rephasing spectra with the phase-twisted lineshapes and their addition yielding pure absorptive features.The sum of the two responses shows eight features arising from the various ladder diagrams contributing to the third-order signals for this six-level system.We see that the diagonal and the cross-peaks consist of two features with opposite signs,separating the dynamics of the ground and first excited states.To correct for the phase mismatch between the signal and the LO fields arising due to pathlength differences,we phase the spectra by fitting the projection of the2D absorption spectrum alongω3to a dispersed pump-probe signal taken with the tracer as the probe under the same conditions[6].Figure2demonstrates the effect of a finiteτ2mixing time on the2D rephasing spectra.The first two panels show the modulation of the cross-peak intensity as a function ofτ2.We see that the intensity of the cross-peak reaches the maximum in Fig.2(a)whenτ2=nπ/2ωas where n is an even integer andωas is the frequency splitting between the symmetric and asymmetric carbonyl stretches.The cross-peaks disappear when n is an odd integer as shown in Fig.2(b).The third panel obtained whenτ2=7050fs indicates the emergence of four new features as a200020502100-ω1/2πc (cm -1)200020502100200020502100(c)(b)(a)-ω1/2πc (cm -1)ωsωaωa ωs ωsωa ωa ωsω3/2πc (c m -1)200020502100ω1/2πc (cm -1)Fig.1.Real part of 2D IR vibrational spectra at τ2=0(a)S I (b)S II and (c)S I +S II .result of various coherent and incoherent population relaxation processes occurring during the mixing time.This results in the diagonal and cross-peaks splitting into three features instead of the usual two features obtained at smaller values of τ2.A systematic study of the 2D rephasing and non-rephasing spectra as a function of τ2allows us to map out the complete dynamics of this multi-level system including the effects of solvent-induced relaxation and populationrelaxation.ωs ωaω3/2πc (c m -1)-ω1/2πc (cm -1)Fig.2.Absolute value 2D IR rephasing spectra as a function of a variable mixing time.(a)τ2=470fs (b)τ2=705fs(c)τ2=7050fs.1.O.Golonzka,M.Khalil,N.Demirdöven,and A.Tokmakoff,“Coupling and orientation between anharmonic vibrations characterized by two-dimensional infrared vibrational spectroscopy,”J.Chem.Phys.,115,10814-10828(2001).2.N.Demirdöven,M.Khalil,O.Golonzka,and A.Tokmakoff,“Correlation effects in two-dimensional vibrational spectroscopy of coupled vibrations,”J.Phys.Chem.A,105,8025-8030(2001).3.D.E.Thompson,K.A.Merchant and M.D.Fayer,“Two-dimensional ultrafast infrared vibrational echo studies of solute-solvent interactionsand dynamics,”J.Chem.Phys.,115,317-330(2001).4.M.T.Zanni,S.Gnanakaran,J.Stenger,and R.M.Hochstrasser,“Heterodyned two-dimensional infrared spectroscopy of solvent-dependent conformations of acetylproline-NH2,”J.Phys.Chem.B,105,6520-6535(2001).5.S.Woutersen,and P.Hamm,“Structure determination of trialanine in water using polarization sensitive two-dimensional vibrational spectroscopy,”J.Phys.Chem.B,104,11316-11320(2000).6.J.D.Hybl,A.Albrecht Ferro and D.M.Jonas,“Two-dimensional Fourier transform electronic spectroscopy,”J.Chem.Phys.,115,6606-6622(2001).。
傅里叶变换
cost comparison: large templates economical
Nc = MN /(2log 2 K + 1) NF
3
periodic noise
Fourier Transformation of Image Data
2、Special Functions Special
2.1 The Complex Exponential Function 2.2 The Dirac Delta Function 2.3 Fourier Series 2.4 The Fourier Transform 2.5 Convolution 2.6 Sampling Theory
16
Fourier Transformation of Image Data
3.1 The Discrete Spectrum
Effect of sampling the spectrum. a Sampled function and its spectrum; b Periodic sequence of impulses used to sample the spectrum (right) and its time domain equivalent (left); c Sampled version of the spectrum (right) and its time domain equivalent (left); the latter is a periodic version of the samples in a. In these F represents an inverse Fourier transformation
∫
f (t )e− jwt dt
基于二维相关中红外光谱技术的邻苯二甲酸二丁酯检测研究
基于二维相关中红外光谱技术的邻苯二甲酸二丁酯检测研究赵丽君;高磊;衣玲学;姜晨;赵昆【期刊名称】《光谱学与光谱分析》【年(卷),期】2017(37)1【摘要】利用二维相关红外光谱技术对正己烷中常用塑化剂邻苯二甲酸二丁酯(DBP)的浓度变化进行了检测研究。
利用傅里叶变换红外光谱仪对溶于正己烷中的DBP 进行检测,得到742,1078,1123,1281,1467,1728,2873,2933和2961 cm-1特征吸收峰。
将红外光谱分为三个波段400~1200,1200~1900和2900~4000 cm-1,通过二维相关光谱分析技术得知在1123 cm-1波段(苯环面外摇摆及 O—C O 单键伸缩运动)、1728 cm-1(C—O 双键的伸缩运动)、2873和2961 cm-1(CH3伸缩运动)以及3436 cm-1(苯环C—H 的面内伸缩运动)对DBP浓度变化比较敏感。
结合红外光谱宏观指纹技术以及二维相关光谱分析方法,能够较准确的分析出正己烷中的DBP的浓度变化,为食品中塑化剂含量的检测以及研究塑化剂的迁移规律提供了新的思路和方法。
%As a kind of Phthalate esters (PEs ),Di-n-butyl phthalate (DBP )is widely employed as plasticizers in the pro-duction of polymeric materials.The concentration variation of DBP/n-hexane solution was studied by monitoring the chroma evo-lution of infrared absorption spectra in conj unction with spectral analysis by using two-dimensional-correlation spectroscopy. Absorption peaks at 742,1 078,1 123,1 281,1 467,1 728,2 873,2 933,2 961 cm-1 was gained with Fourier transform in-frared spectra.The IR spectra was divided into three bands:400~1 200,1 200~1 900 and 2 900~4 000 cm-1 ,correlation be-tween the absorption peaks and the sequential order of the changes in spectral intensity extracted from synchronous and asyn-chronous plots indicated that some bong vibrations in 1 123 cm-1 (Benzene ring surface vibration and O—C O bending vibra-tion ),1 728 cm-1 (C—O bending vibration),2 873,2 961 cm-1 (CH3 concertina movement )and 3 436 cm-1 (C—H bending vibration in plane of Benzene)is sensitive to the concentration of DBP.This result showed that the chroma evolution of infrared absorption spectra in conj unction with spectral analysis using two-dimensional-correlation spectroscopy can accurately analyze the concentration of DBP in n-hexane.This research provides a theoretical basis to the detection and analysis of DBP.【总页数】5页(P109-113)【作者】赵丽君;高磊;衣玲学;姜晨;赵昆【作者单位】油气光学探测技术北京市重点实验室，中国石油大学北京，北京102249;油气光学探测技术北京市重点实验室，中国石油大学北京，北京 102249;油气光学探测技术北京市重点实验室，中国石油大学北京，北京 102249;油气光学探测技术北京市重点实验室，中国石油大学北京，北京 102249;油气光学探测技术北京市重点实验室，中国石油大学北京，北京 102249【正文语种】中文【中图分类】O433.4【相关文献】1.基于二维相关中红外光谱技术的无创血糖检测特异性研究 [J], 张雯;曹玉珍;刘蓉;徐可欣2.基于二维相关近红外光谱技术测定辅料十二烷基硫酸钠 [J], 郝远;方洪壮;韩君;杨玉婷;李淑贤3.中红外光谱技术在牛奶营养物质预测及奶牛相关特性分析上的应用 [J], 董利锋;YAN Tianhai;屠焰;刁其玉4.基于中红外吸收光谱技术测量高温流场CO浓度研究 [J], 胡尚炜;殷可为;涂晓波;杨富荣;陈爽5.基于中红外激光吸收光谱技术的微量乙炔检测研究 [J], 刘立富;冯雨轩;陈东;晏明月;吴强因版权原因，仅展示原文概要，查看原文内容请购买。
王青云-生物神经元网络动力学的研究进展
Intelligent Robots
19:06:04
Neural Computers
Biological Control
Neural Medical Techniques
6 6
Structure of Single Neuron
A basic element for information processing in nervous systems. There are about 1011 neurons in the human brain and 104 synapses for a neuron.
19:06:04
O (2008) Mapping the structural core of human cerebral cortex. PLoS Biology 15 Vol. 6, No. 7, e159
Neuronal networks
•Neuronal networks involve a large number of individual neurons. •Details of the connectivity not usually known. •Hard to analyze how connectivity influences ODE dynamics.
(Li Li, Ren Wei et al, IJBC, 2004. Duan Li Xia et al, Neurocomputing 2008)
Chay model
19:06:04
10
Chaos (in experimental neural pacemakers)
between period 2 and period 3 firings (Ren Wei, IJBC, 1997)
ch4 _Image enhancement in the Frequency Domain
Inverse Fourier transform (IDFT)
f ( x, y ) F (u, v)e j 2 (ux / M vy / N )
u 0 v 0
M 1 N 1
for x 0,1,2,..., M 1, y 0,1,2,..., N 1
• u, v : the transform or frequency variables • x, y : the spatial or image variables
The one-dimensional Fourier transform and its inverse (discrete time case) Fourier transform (DFT)
1 F (u ) M
M 1 x 0
f ( x)e
j 2 ux / M
for u 0,1, 2,..., M 1
Please note the relationship between the value of K and the height of the spectrum and the number of zeros in the frequency domain.
Harbin Engineering University
Techniques are based on modifying the
Fourier transform of an image
Harbin Engineering University
Digital Image Processing
Chapter4 Image enhancement in the Frequency Domain
草乌类蒙药的红外光谱分析与鉴定
草乌类蒙药的红外光谱分析与鉴定苏都娜;策力木格;松林;聂波;图雅【摘要】目的:对蒙药草乌根、草乌叶、草乌花、草乌芽的原药材及其总生物碱提取物进行分析.方法:采用红外光谱的三级鉴定方法(红外光谱、二阶导数谱以及二维相关谱)进行样品的全成分分析.结果:草乌根的谱图与淀粉的标准谱图相似,出现淀粉特征峰1 155、1 070、1 019 cm-1,故草乌根含有大量淀粉;叶、花、芽含芳香类物质较多(1 600 cm-1),糖苷类物质(1 050-1 070 cm-1)、酯类物质不明显;草乌花、草乌叶、草乌芽的红外谱图中能够观察到芳香环(1 595 cm-1附近)和=C-O(1 262 cm-1附近)有特征吸收,证明三者共有成分为二萜类生物碱.二阶导数谱图显示,根在1 712 cm-1 (C=O)附近的特征峰明显强于花、叶和芽,说明根中二萜类生物碱类成分含量高于花、叶和芽;二维谱图在800-1 300 cm-1处根有6个自动峰1 745、1 650、1 560(最强)、1 465、1400、1300 cm-1;叶、芽、花相似其自动峰有1680、1560(最强)、1465 cm-1.结论:红外光谱宏观指纹技术可提供大量整体信息,能够较准确的把握草乌类药材的整体质量.红外光谱法和二维相关光谱提供了大量草乌、草乌花、草乌叶、草乌芽的整体结构信息,验证了4种药材所含物质结构和含量的差异,为今后草乌的系统研究工作奠定基础.%The radix,leaf,flower and bud of raw medicinal materials and extraction of total alkaloids of Aconitum kusnezoffii Reichb.were all involved in this investigation.All the compositions from the samples were analyzed through fourier transform infrared spectroscopy (FTIR) combined with second derivative IR spectroscopy and two-dimensional IR correlation spectroscopy (2D-IR).It was found that the spectra of raw medicinal materials showed that the radix of A.kusnezoffii Reichb.featuring a large quantity of starch was thesame as starch with the characteristic peaks at 1,155,1,070 and 1,019.The leaf,flower and bud contained the similar aromatic hydrocarbons(1,600),glycosides (1,050-1,070),while lipids were not clear.The characteristic peaks of the buds,flowers and leaves were all at 1,595 cm-1 (vibration of phenyl framework) and 1,262 cm-1 (=C-O).Therefore,it was suggested that the common compound of the three parts be diterpenoid alkaloids.Second derivative IR spectroscopy showed that the characteristic peaks of radix was stronger than those of the flower,leaf and bud at 1,712 cm-1 (C=O),which proved that the quantity of characteristic peaks in the radix was larger than those in the flower,leaf and bud.In addition,six autopeaks at 1,745,1,650,1,560 (the most strong),1,465,1,400,1,300 were detected from the radix.The similar autopeaks at 1,745,1,650,1,560 (the most strong),1,465,1,400,1,300 were found in the leaf,bud and flower.In conclusion,it was demonstrated that the macro-fingerprint infrared spectroscopic identification method provided a large quantity of the comprehensive information and entirely grasped the quality ofA.kusnezoffii Reichb.Besides,FTIR and 2D-IR provided massive information of the integral structures of the radix,leaf,flower and bud of A.kusnezoffii Reichb.and verified the differences between the four parts of the herb in physical structure and the contents,laying a foundation for further systematic work.【期刊名称】《世界科学技术-中医药现代化》【年(卷),期】2016(018)012【总页数】6页(P2170-2175)【关键词】红外光谱;二阶导数谱;二维相关光谱;草乌【作者】苏都娜;策力木格;松林;聂波;图雅【作者单位】内蒙古民族大学蒙医药学院通辽028000;内蒙古医科大学蒙医药学院呼和浩特010110;内蒙古医科大学蒙医药学院呼和浩特010110;北京中医药大学东直门医院北京100027;中国中医科学院中医药发展研究中心北京100700【正文语种】中文【中图分类】R284蒙药草乌类药材指毛茛科植物北乌头Aconitum kusnezoffii Reichb.的干燥花（蒙药名：“草乌花”）、芽（蒙药名：“草乌芽”）、叶（蒙药名：“草乌叶”）、母根（蒙药名：“草乌”），均具有杀“粘”、止痛、燥“协日乌素”之功效，用于“瘟、粘、奇哈、刺痛、结喉、痧症、痛风、游痛证、关节”协日乌素、风湿病、心“赫依”、牙痛等症，为蒙医临床常用药[1]。
Fourier Transform Basics
f t
F n e f t e
j 2 pnt
dn dt
F n
j 2 pnt
Waves: 5
PROPERTIES OF FOURIER TRANSFORMS
Fourier transforms are sometimes of use in physics due to their direct physical interpretation (see later), but often their usefulness is more indirect
In particular, a great usefulness comes from their help in solving awkward differential equations
Here we list several general transform properties of benefit in this and other contexts (Note that these properties are listed here without proofs. Most proofs follow from the defining equations)
The othorgonality relations:
0 2p
0
cos m cos n d 0 p
mn mn mn mn
0 2p
0
sin m sin n d 0 p
0 2p
0
sin m cos n d 0 (all m,n)
Waves: 5
Waves: 5
二元函数的离散二维傅里叶变换与离散二维傅里叶变换的应用
二元函数的离散二维傅里叶变换与离散二维傅里叶变换的应用二元函数的离散二维傅里叶变换（Discrete Two-dimensional Fourier Transform）是一种将二维离散信号转换到频域的重要数学工具。
在数字图像处理、通信系统和信号处理等领域中得到了广泛应用。
本文将介绍二元函数的离散二维傅里叶变换的定义、性质以及其在数字图像处理中的应用。
一、离散二维傅里叶变换的定义和性质离散二维傅里叶变换是二维信号的频域表示，它将一个二元函数表示为两个离散变量的函数。
设f(m,n)是一个m×n的离散二维信号，则它的离散二维傅里叶变换F(u,v)定义为：F(u,v)=∑[∑f(m,n)e^(-j2π(um/M+vn/N))] (1)其中，u和v是频率变量，范围在[0,M-1]和[0,N-1]之间，M和N分别表示信号的行数和列数。
离散二维傅里叶变换有以下性质：1. 线性性质：设f1(m,n)和f2(m,n)是两个m×n维的离散二维信号，α和β是常数，则有F(αf1(m,n)+βf2(m,n))=αF(f1(m,n))+βF(f2(m,n))。
2. 变换的逆运算：假设一个信号F(u,v)经过离散二维傅里叶变换得到一个函数f(m,n)，则信号F(u,v)通过逆变换可以得到相应的函数f(m,n)，即f(m,n)=∑[∑F(u,v)e^(j2π(um/M+vn/N))]。
3. 位移性质：对于一个二维离散信号f(m,n)的傅里叶变换F(u,v)，其在频域中的相对位移可以引起在空域中的相位变换。
即若f(m,n)经过水平或垂直平移变换，则其傅里叶变换F(u,v)也会在相应的方向上发生相位变化。
4. 共轭对称性：离散二维傅里叶变换满足共轭对称性质，即对于一个二维离散信号f(m,n)的傅里叶变换F(u,v)，有F(u,v) = F*(-u,-v)，其中F*(-u,-v)表示F(u,v)的共轭复数。
二、离散二维傅里叶变换在数字图像处理中的应用离散二维傅里叶变换在数字图像处理中有广泛的应用，包括图像滤波、边缘检测、图像增强等。
二维Fourier变换及其作用
二维Fourier变换及其作用论文题目：二维Fourier变换及其作用指导老师：熊向团姓名：骆盼学号：201172020223E–ma i l：1234567890@【内容提要】19世纪初，傅里叶在向巴黎科学院呈交的关于热传导的著名论文中提出了傅里叶级数傅里叶分析方法已经广泛用于物理学及工程学科的各个领域。
傅立叶变换能将满足一定条件的某个函数表示成三角函数（正弦和/或余弦函数）或者它们的积分的线性组合。
在不同的研究领域，傅立叶变换具有多种不同的变体形式，如连续傅立叶变换和离散傅立叶变换。
最初傅立叶分析是作为热过程的解析分析的工具被提出的。
【关健词】傅里叶级数，二维离散傅立叶变换，快速傅立叶变换AbstractIn the early 19th century, Fourier, shall be submitted to the Paris academy of sciences of heat conduction of the thesis put forward the famous Fourier series Fourier analysis method has been widely used in various fields of physics and engineering disciplines. Fourier transform can meet certain conditions is expressed as a function of trigonometric function (sine and/or cosine function) or a linear combination of the integral. In different fields of study, a variation of the Fourier transform has many different forms, such as continuous Fourier transform and discrete Fourier transform. Initial Fourier analysis is a tool for as analytical analysis of thermal process was proposed.Key wordsFourier series, the two-dimensional discrete Fourier transform, fast Fourier transform目录一.预备知识：1.三角函数系的正交性 (4)2.(函数展开成)傅里叶级数 (4)3.狭里克雷(Dirichlet)收敛定理 (5)二.引入傅里叶变换的定义 (7)三.离散的傅立叶变换 (7)1.一维离散变换 (7)2.二维离散变换 (8)3.二维离散傅立叶变换的性质 (8)（一）平均值 (8)（二）变换域的周期性 (8)（三）对称共轭性 (9)（四）平移性 (9)（五）分配性和比例性 (9)（六）可分离性 (9)（七）旋转性质 (10)（八）微分性质 (10)四.快速傅立叶变换（FFT） (11)五.离散图像变换的一般表达 (14)1.离散图像变换的代数表达式 (14)2.离散图像变换的矩阵表达式 (15)六.编程实验 (17)参考文献............................................................20 致谢 (20)傅里叶变换(Fourier transform )傅里叶变换是一种分析信号的方法，它可分析信号的成分，也可用这些成分合成信号。
BIT医学图像答案2015.1.24
医学图像答案1. Image terminology explanation（医学图像术语解释）(1) image smoothing（图像平滑）Image smoothing is used to highlight the image of wide area, the low frequency component, trunk or suppress image noise and interference of high frequency components, make the image brightness flat gradient, gradient decrease mutations, improve the image quality of the image processing methods.Image smoothing methods include: interpolation method, linear smoothing method, convolution method and so on.(2)image sharpening（图像锐化）Image sharpening is to compensate the image contour, enhancing image edge and gray level jump, images by an average or integral operation, thus on the inverse operation, make the image clear.Image sharpening method includes: gradient method and Laplace algorithm, Robert algorithm and so on.(3)low-pass filter（低通滤波器）A low-pass filter is a filter that passes signals with a frequency lower than a certain cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The amount of attenuation for each frequency depends on the filter design.(4)high-pass filter（高通滤波器）A high-pass filter is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency depends on the filter design. A high-pass filter is usually modeled as a linear time-invariant system. It is sometimes called a low-cut filter or bass-cut filter.High-pass filters have many uses, such as blocking DC from circuitry sensitive to non-zero average voltages or radio frequency devices.(5)image restoration（图像复原）Image restoration is the operation of taking a corrupted/noisy image and estimating the clean original image. Corruption may come in many forms such as motion blur, noise, and camera misfocus.Image restoration is different from image enhancement in that the latter is designed to emphasize features of the image that make the image more pleasing to the observer, but not necessarily to produce realistic data from a scientific point of view.(6)image segmentation（图像分割）image segmentation is the process of partitioning a digital image into multiple segments (sets of pixels, also known as superpixels). The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. Image segmentation is typically used to locate objects and boundaries (lines, curves, etc.) in images. More precisely, image segmentation is the process of assigning a label to every pixel in an image such that pixels with the same label share certain characteristics.The result of image segmentation is a set of segments that collectively cover the entire image, or a set of contours extracted from the image (see edge detection). Eachof the pixels in a region are similar with respect to some characteristic or computed property, such as color, intensity, or texture. Adjacent regions are significantly different with respect to the same characteristic(s).When applied to a stack of images, typical in medical imaging, the resulting contours after image segmentation can be used to create 3D reconstructions with the help of interpolation algorithms like Marching cubes.(7) image registration（图像配准）Image registration is to different time, different sensors (imaging equipment) or under different conditions (weather, illumination, camera position and Angle, etc.) to obtain two or more image matching, superposition, the process of image registration is to point to in a medical image to seek a space (or a series of transformation, to make it with another medical image is the same on the corresponding points to the space.2.Write down the 2D Discrete Fourier transform, and discuss the relationship between the frequency components of the Fourier transform and spatial features of an image.（写出二维离散傅里叶变换，并讨论图像的傅里叶变换的频率分量与空间特性之间的关系）The 2D DFT F(u,v) can be obtained by:(1) taking the 1D DFT of every row of image f(x,y), F(u,y), (2)taking the 1D DFT of every column of F(u,y).Frequency is directly related to rate of change. The frequency of fast varying components in an image is higher than slowly varying components.The high frequency part reflects the details information(variance of gray level) of image, The low frequency part reflects the general gray-level appearance.3.What is image histogram? Which areas of histogram can be used in? What is the basic concept of histogram equalization?（什么是图像（灰度）直方图？有哪些用途？直方均衡的基本思想是什么？）Image histogram：Gray histogram is a function of grayscale, describes the number of each pixel gray levels in the image, reflect the frequencies of each gray level images.Here is a grayscale, ordinate is frequency of gray levels. Purpose: evaluation of imaging conditions, image enhancement, image segmentation, image compression, extends the conditional histogram, the joint histogram etc.The basic concept of histogram equalization：the basic idea of histogram equalization of the basic idea is to put the original figure is evenly distributed in the form of a histogram transformation, thus increasing the dynamic range of pixel gray value which can achieve the result that to enhance the overall image contrast.4.What is image enhancement in the frequency (spatial) domain? List the some of the main methods of frequency (spatial) enhancement.（什么是频率域的图像增强，什么是空间域的图像增强？列出两者各有哪些主要方法）Image enhancement：According to the specific need to highlight certain parts of the image information, at the same time, to weaken or remove some unwantedinformation processing method.Image enhancement methods: image enhancement in the spatial domain and frequency domain image enhancement.image enhancement in the frequency domain ：The image as a two-dimensional signal, carries on the two-dimensional Fourier transform, the image of a frequency domain transform coefficient for processing, then enhanced images were obtained through the inverse transformation.Frequency domain image smoothing and fuzzy mainly through the low-pass filter of high frequency attenuation.While sharpening image mainly by high frequency filter filter out low frequency.Main methods : high-pass filter, low-pass filter and homomorphic filtering enhancement method;image enhancement in the spatial domain ：Spatial domain method:In space domain of image point operations, it can allow users to change the grey value of pixels in the image, so through some processing will create a new image.Main methods : average filtering method, the median filtering method, gradient method, mask matching method, the statistical difference method.5. Write the mathematical model of image restoration, explain the main cause of image degeneration, and list some main image restoration methods.（写出图像复原的数学模型，解释图像降质的主要原因，并列出图像复原的主要方法）mathematical model ：For an input image f (x, y) for processing, to produce a picture of a degraded image g (x, y).A given g (x, y) and some knowledge about the degradation function H as well as some knowledge of additive noise item, a recovery filter is designed, the purpose of image restoration is for an estimate of the original image ),(y x f .the main cause of image degeneration ：Image degradation mainly comes from image Retrieval and transmission process: Retrieval process: as the optical imaging system aberration, diffraction, nonlinear distortion, defocusing, nonlinear, imaging process of photosensitive components of relative motion, atmospheric turbulence effect, environmental factors of random noise,will make the image produces a certain degree of degradation;Transmission process: due to the transmission channel interference to lower image quality.image restoration methods：1. Spatial filtering restoration (the only degradation is noise): mean filters, order statistic filter, the adaptive filter;2.The frequent filtering (to eliminate the periodic noise): band stop filter, bandpass, notch filtering, optimal notch filter;3. Estimating the degradation function;4. The inverse filtering;5. The minimum mean square error (mse);6. The constrained least squares filtering;7. The geometric mean filter；6.Give major medical imaging techniques, and take examples in clinical applications.（列出主要的医学成像技术，并给出临床应用实例）In modern medicine, medical imaging has undergone major advancements. Today, this ability to achieve information about the human body has many useful clinical applications. Over the years, different sorts of medical imaging have been developed, each with their own advantages and disadvantages.X-ray based methods of medical imaging include conventional X-ray, computed tomography (CT) andmammography. To enhance the X-ray image, contrast agents can be used for example for angiography examinations.Molecular imaging is used in nuclear medicine and uses a variety of methods to visualize biological processes taking place in the cells of organisms. Small amounts of radioactive markers, called radiopharmaceuticals, are used for molecular imaging.Other types of medical imaging are magnetic resonance imaging (MRI) and ultrasound imaging. Unlike conventional X-ray, CT and Molecular Imaging, MRI and ultrasound operate without ionizing radiation. MRI uses strong magnetic fields, which produce no known irreversible biological effects in humans.Diagnostic ultrasound systems use high-frequency sound waves to produce images of soft tissue and internal body organs.Imaging using X-raysX-ray imaging uses an X-ray beam that is projected on the body. When passing through the body, parts of the x-ray beam are absorbed. On the opposite side of the body, the X-rays are detected, resulting in an image.Molecular ImagingMolecular imaging provides detailed information of the biological processes taking place in the body at cellular and molecular levels and can indicate disease in its earliest stages.Other Types of Medical ImagingSome types of medical imaging work without using ionizing radiation, for example magnetic resonance imaging (MRI) and ultrasound imaging, and have specific uses in the diagnosis of disease.7. The physics, characteristics, advantage and disadvantage, and clinical applications of X-ray, MR, NMI, US.（基本原理、特点、优势、不足、临床应用）（1）X-ray(X射线)The physics:When a roughly uniform beam intensity X-ray exposure to human body, one part of X-ray absorption and scattering, the other part along the direction of the original transmission through the human body. Due to the human body all kinds of tissue and organ differences in density, thickness and so on , the absorption amount of projection on the X ray of each are not identical, so that the human body through X-ray intensity distribution change and carry human body information, and forming X-ray image information eventually. Namely for X ray imaging body.Characteristics：X-ray image information cannot identify for the human eye, it must pass a certain collection, conversion, display system of X-ray intensity distribution is converted into visible light intensity distribution, formation of X ray image visible to the human eye. Advantage：It has high resolution, which can clear the organ and structure development, and can clearly show the lesions;Disadvantage：(1) High-energy gamma ray source can cause irreversible damage to the human body tissue and the environment, even the medical X-ray CT, the accumulation of multiple use, X ray will have influence on patient is according to the organization.(2) Due to X-ray computed tomography (ct) imaging rather rely on intravenous contrast agent to development, so there is a potential danger, which may make some patients of renal injury.Clinical applications：1、Diagnosis: according to different human groups of X-ray absorption and transmittance, using high sensitivity of the instrument to measure to the human body, so that it can be taken under the body section of the inspected or stereo image, and find small lesions in any parts of the body.2、Treatment: X-rays through the body's tissues could produce ionization effect, Compton scattering, and generates electron pair, which may induce a series of biological effects.Research shows that X-ray has damage to the biological tissues, especially for the separatist activities or is the division of the cell, its damage ability is stronger.（2）MR（Magnetic Resonance磁共振）The physics：MR is the use of nuclear magnetic resonance (NMR) principle, through extra gradient magnetic field to detect the electromagnetic waves which is emitted by objects, and use it to drow into objects within the structure of the image.The imaging of the medical is the use of hydrogen nuclei in the body's tissues (protons) in magnetic field by rf pulse excitation and nuclear magnetic resonance phenomenon, produce magnetic resonance (NMR) signal, through computer processing, gives a certain level of human body image reconstruction imaging techniques.Characteristics：1、Multi-parameter imaging, it can provide abundant diagnostic information;2、High contrast imaging, it can she come to the anatomy atlas;3、Implementation from the three dimensional space observation of human body;4、Human energy metabolism,it may directly observe the biological blueprint of cell activity;5、Do not use contrast medium, it can observe the heart and blood vessels structure;6、No ionizing radiation, it can be involved in magnetic resonance imaging (MRI) treatment;7、Without the disturbance of gas and bone artifacts;Advantage：(1)without radioactive damage to human body’s organization, also do not have the biological damage;(2)soft tissue density resolution is higher than that of CT, the spatial resolution can be equivalent to that of CT.(3)It can directly do the transverse, sagittal and coronal layer and a variety of cant image;(4)More imaging parameters and methods, and more diagnostic information than CT;(5)With the help of the proton flow effect, it can clearly show that blood vessels; Disadvantage：(1)Calcification and bone disease cannot display oven;(2)Scan for a long time, daily can check the number of relatively less CT;(3)On abdominal MRI remains motion artifact interference;(4)In the body of magnetic metals cannot check;(5)It is too expensive.Clinical applications：Magnetic resonance imaging (MRI) has been used throughout the system of imaging diagnosis.Effect is the best brain, and spinal cord, heart, great vessels, joint and pelvic bone, soft tissue.For cardiovascular disease can not only observe the chamber, great vessels and valvular anatomy changes, and can make ventricular analysis, qualitative and semi-quantitative diagnosis, can make multiple sectional drawing, high spatial resolution, a heart and lesions, and its relationship with surrounding structures.In diagnosis of cerebrospinal lesions, can make coronal, sagittal and transverse section. （3）NMI（Nuclear Medical Imaging核医学成像）The physics：Introducing a radioactive isotope labeling on the drugs and into the body, when it is absorbed by the body's organs and organizations, formed the radiation source in the body.From the body in vitro were tested by nuclear detection device can rays emitted by isotope in the process of decay, radioactive isotope distribution density of the image in the body.Due to radioactive drugs remain relatively stable nuclide or marked the chemical properties and biological behavior of drugs, normally involved in the metabolism of the body, so the radioisotope images not only reflect the viscera and organization form, more important is to provide the related viscera function and related physiological, biochemical information.Characteristics：It can provide both morphological and functional of the organ or tissue.Advantage：(1) High specificity;(2) The whole body imaging;(3) Good safety;Disadvantage：It is the main problem is the price of the equipment is too high, and need to form a complete set of cyclotron to generate the required super short half-life positron tracer, which means the hospital must be equipped with cyclotron.Clinical applications：Use PET imaging, it should be injected in the patient of radioactive drugs, radioactive drugs release signals in a patient, and received by in vitro of the PET scanner, then to form images, it can appear organ or tissue chemical change, the degree of the metabolism of a portion of the pointed out that different from the norm.（4）US（UltraSound超声成像）The physics:Various organs and organizations has its specific acoustic impedance and attenuation characteristics, and therefore constitute the difference on the acoustic impedance and attenuation differences.When the ultrasonic into the body, from surface to the deep, will go through with different acoustic impedance and attenuation characteristics of different organs and tissues, resulting in a different reflection and attenuation.The different reflection and attenuation is the basis of the composition of ultrasonic bining with the received echo, according to the echo intensity, with different shades of light show on the screen, in turn, it can show section ultrasound images of the human body, called the ultrasonographic (sonogram or echogram). Characteristics：Ultrasonic imaging is an ultrasonic acoustic properties can obtain the internal structure of human organs, ultrasonic imaging technology will these information into image viewable to the human eye, so as to checking methods for the diagnosis of disease.Advantage：(1) Good real-time;(2) No damage;(3) There is no pain;(4) Low cost;Disadvantage：The contrast of the image resolution and space resolution is lower than CT and MRI. Clinical applications：Ultrasonic diagnosis foundation focuses on the detailed observation and analysis.Capture a variety of features, comprehensive analysis of the cause, the various changes in physiological condition, and combined with other forms of diagnosis.。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
Periodicity of Helicopter Noise
The main rotor-tail rotor ratio, the multiple of tail rotor rotational frequency in relation to the main rotor rotational frequency, is never designed to be a whole number. This prevents the harmonics of the two rotors from reinforcing each other and resonating. Thus the noise from these two rotors can be characterized as the sum of two periodic signals with incommensurate frequencies. It is shown theoretically in [4] that this summed signal is not periodic. Errors described in ref. [9] would result if the 1-D Fourier transform is used on a non-periodic signal. Therefore, Hardin and Miamee proposed in [4] that a 2-D Fourier transform would better characterize the signal. The following section discusses the 2-D Fourier transform and explains how it may be used to distinguish main rotor noise from tail rotor noise more clearly. Section III shows preliminary 2-D Fourier transform analyses performed on simulated signals to indicate what "ideal" 2-D spectra should look like. Section IV describes the helicopter acoustics flight test from which data is analyzed. Section V shows the results of 2-D Fourier transform analysis on the measured flyover data, followed by conclusions in Section VI. The advantages of 2-D Fourier transform analysis on helicopter flyover acoustic data are also discussed in Section VI.
TWO-DIMENSIONAL FOURIER TRANSFORM ANALYSIS OF HELICOPTER FLYOVER NOISE
Odilyn L. Santa Maria, F. Farassat NASA Langley Research Center Hampton, VA Philip J. Morris The Pennsylvania State University State College, PA
E[•] Expected value
ABSTRACT
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
Presented at the American Helicopter Society 55th Annual Forum, Montreal, Quebec, May 25 oise propagates to the ground.
This information can be used to create an illustration or graphic that visualizes the acoustics of a helicopter. The graphic could then be a tool used to identify the areas (flight operations, blade tips, etc) to modify in order to reduce the noise for the listener. The researcher is thus challenged to create this illustration or graphic that efficiently conveys the most relevant information. The purpose of this paper is to identify the advantages of using a 2-D Fourier transform to visualize helicopter flyover noise. Results from this particular 2-D analysis were first introduced in [1]. To explore the possibilities of the 2-D Fourier transform, this paper will provide the 2-D spectra from two different helicopters: one with a tail rotor, and one without. These data, collected during an acoustic flight test in 1996, will be shown using conventional analysis methods, namely the FFT, as well as with the 2-D Fourier transform. The 2-D Fourier transform will be used as an alternate method to distinguish main rotor and tail rotor noise.
Some studies have targeted the wakes and tip vortices shed by the main rotor blades. These wakes and tip vortices not only generate blade-wake interaction and the highly impulsive blade-vortex interaction noise when they encounter other main rotor blades, but they can also encounter the tail rotor blades and generate main rotor-tail rotor interaction noise.