ConvolutionofSignalsinMATLAB

RobertFrancis

August 29, 2011August29,2011

Review of ConvolutionReviewofConvolution

dthxthtxty )()()(*)()(

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Review of ConvolutionReviewofConvolution

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Smith, http://www.dspguide.com/ch6/2.htm

Generating Time Vectors in MatlabGeneratingTimeVectorsinMatlab

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Generate Square WaveGenerateSquareWave

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Plot Square WavePlotSquareWave

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Adjust Magnitude and ReplotAdjustMagnitudeandRe plot

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Nyquist Sampling TheoremNyquist SamplingTheorem

If a continuous time signal has no frequencyIfacontinuoustimesignalhasnofrequencycomponentsabovefh,thenitcanbespecifiedby a discrete time signal with a samplingbyadiscretetimesignalwithasamplingfrequencygreaterthantwicefh.

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Define Nyquist Sampling Time VectorDefineNyquist SamplingTimeVector

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Generate Nyquist Sampling Square WaveGenerateNyquist SamplingSquareWave

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Plot Nyquist Square WavePlotNyquist SquareWave

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Define Undersampled Time VectorDefineUndersampled TimeVector

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Generate Undersampled Square WaveGenerateUndersampled SquareWave

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Plot UndersampledPlotUndersampled

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Convolution With Linear Decay SignalConvolutionWithLinearDecaySignal

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Linear Decay SignalLinearDecaySignal

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Plot of ConvolutionsPlotofConvolutions

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Convolution with Exponential Decay SignalConvolutionwithExponentialDecaySignal

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Exponential Decay SignalExponentialDecaySignal

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Plot of ConvolutionsPlotofConvolutions

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FFT of Signals in MATLABFFTofSignalsinMATLAB

RobertFrancis

August 31, 2011August31,2011

Review of Fourier TransformReviewofFourierTransform

dtetxfX ftj 2)()(The Fourier Integral

DFT (Discrete Fourier Transform)

1

0

/2 ,...,2,1,N

n

Nknjnk NkexX

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