交大413信號系統(tǒng)與信號處理教學(xué)課件第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=12兩個序列周期不同789Forarealsequence:10FIGURE8.2EXAMPLE.實序列的DFS1112Figure8.3圖解法求周期卷積138.4fourierrepresentationoffinite-durationsequences:

DefinitionofthediscretefouriertransformFigure8.8EXAMPLE.1415Figure8.10EXAMPLE.以5為周期延拓168.5samplingthefouriertransformEXAMPLE.Figure8.5以10為周期延拓17188.6propertiesofthefouriertransform2.circularshiftofasequence19Figure8.12EXAMPLE.圖示循環(huán)移位20EXAMPLE.214.Symmetryproperties:22Forarealsequence:23N=10EXAMPLE.實序列的DFT245.circularconvolution25Figure8.14EXAMPLE.圖解法求循環(huán)卷積26Figure8.15N=LEXAMPLE.卷積結(jié)果與N有關(guān)27Figure8.16N=2LEXAMPLE.286.paswal’stheory298.7linearconvolutionusingthediscretefourier transform30NpointsampleIDFT根據(jù)循環(huán)卷積性質(zhì)根據(jù)頻域取樣FTPROVE31Figure8.18EXAMPLE.線性卷積線性卷積右移線性卷積左移6點循環(huán)卷積=線性卷積混迭12點循環(huán)卷積=線性卷積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周期序列的傅里葉變換

8.3DFS的性質(zhì)

8.4有限長序列的DFT 8.5DFT是FT的采樣

8.6DFT的性質(zhì)

8.7用DFT實現(xiàn)線性卷積

8.8DCT

小結(jié)41要求：

DFS的定義，計算和性質(zhì)

DFT定義的引出：DFS或頻