交大413信号系统与信号处理教学课件第08章

18.1representationofperiodicsequences:thediscretefourierseries8.2thefouriertransformofperiodicsignals8.3propertiesofthediscretefourierseries8.4fourierrepresentationoffinite-durationsequences:

Definitionofthediscretefouriertransform8.5samplingthefouriertransform(pointofsampling)8.6propertiesofthefouriertransform8.7linearconvolutionusingthediscretefouriertransform8.8thediscretecosinetransform(DCT)Chapter8thediscretefouriertransform28.1representationofperiodicsequences:

thediscretefourierseries3Figure8.1EXAMPLE.N=104Figure8.258.2thefouriertransformofperiodicsignals68.3propertiesofthediscretefourierseriesN=4N=6N=12两个序列周期不同789Forarealsequence:10FIGURE8.2EXAMPLE.实序列的DFS1112Figure8.3图解法求周期卷积138.4fourierrepresentationoffinite-durationsequences:

DefinitionofthediscretefouriertransformFigure8.8EXAMPLE.1415Figure8.10EXAMPLE.以5为周期延拓168.5samplingthefouriertransformEXAMPLE.Figure8.5以10为周期延拓17188.6propertiesofthefouriertransform2.circularshiftofasequence19Figure8.12EXAMPLE.图示循环移位20EXAMPLE.214.Symmetryproperties:22Forarealsequence:23N=10EXAMPLE.实序列的DFT245.circularconvolution25Figure8.14EXAMPLE.图解法求循环卷积26Figure8.15N=LEXAMPLE.卷积结果与N有关27Figure8.16N=2LEXAMPLE.286.paswal’stheory298.7linearconvolutionusingthediscretefourier transform30NpointsampleIDFT根据循环卷积性质根据频域取样FTPROVE31Figure8.18EXAMPLE.线性卷积线性卷积右移线性卷积左移6点循环卷积=线性卷积混迭12点循环卷积=线性卷积32Conclusion:(2)calculatelinearconvolutionbycircularconvolution(1)calculateNpointcircularconvolutionbylinearconvolution(3)calculatelinearconvolutionbyDFT33Figure8.22implementinglineartime-invariantFIRsystemsusingtheDFT

34Figure8.23overlap-addmethod

35Figure8.24overlap-savemethod

368.8thediscretecosinetransform(DCT)37DCT-1DCT-23839ComparewithDFT:energycompactionpropertyDCTDFT40

第8章DFT 8.1周期序列的DFS 8.2周期序列的傅里叶变换

8.3DFS的性质

8.4有限长序列的DFT 8.5DFT是FT的采样

8.6DFT的性质

8.7用DFT实现线性卷积

8.8DCT

小结41要求：

DFS的定义，计算和性质

DFT定义的引出：DFS或频