Convolution of Signals in MATLAB.pdf

Convolution of Signals in MATLAB

Robert Francis

August 29, 2011August 29, 2011

Review of ConvolutionReview of Convolution

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

9/12/2011Visual example copied from Wikipedia

Review of ConvolutionReview of Convolution

9/12/2011

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

Generating Time Vectors in MatlabGenerating Time Vectors in Matlab

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Generate Square WaveGenerate Square Wave

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Plot Square WavePlot Square Wave

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Adjust Magnitude and Re‐plotAdjust Magnitude and Re plot

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Nyquist Sampling TheoremNyquist Sampling Theorem

• If a continuous time signal has no frequencyIf a continuous time signal has no frequency components above fh, then it can be specified by a discrete time signal with a samplingby a discrete time signal with a sampling frequency greater than twice fh.

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Define Nyquist Sampling Time VectorDefine Nyquist Sampling Time Vector

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Generate Nyquist Sampling Square WaveGenerate Nyquist Sampling Square Wave

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Plot Nyquist Square WavePlot Nyquist Square Wave

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Define Undersampled Time VectorDefine Undersampled Time Vector 

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Generate Undersampled Square WaveGenerate Undersampled Square Wave

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Plot UndersampledPlot Undersampled

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Convolution With Linear Decay SignalConvolution With Linear Decay Signal

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Linear Decay SignalLinear Decay Signal

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Plot of ConvolutionsPlot of Convolutions

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Convolution with Exponential Decay SignalConvolution with Exponential Decay Signal

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Exponential Decay SignalExponential Decay Signal

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Plot of ConvolutionsPlot of Convolutions

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FFT of Signals in MATLABFFT of Signals in MATLAB

Robert Francis

August 31, 2011August 31, 2011

Review of Fourier TransformReview of Fourier Transform

dtetxfX ftj 2)()(The Fourier Integral

DFT (Discrete Fourier Transform)

1

0

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

n

Nknjnk NkexX

9/12/2011