convolution of signals in matlab - the university of …dlm/3350 comm sys/convolution of signals...
TRANSCRIPT
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
9/12/2011
Generate Square WaveGenerate Square Wave
9/12/2011
Plot Square WavePlot Square Wave
9/12/2011
Adjust Magnitude and Re‐plotAdjust Magnitude and Re plot
9/12/2011
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.
9/12/2011
Define Nyquist Sampling Time VectorDefine Nyquist Sampling Time Vector
9/12/2011
Generate Nyquist Sampling Square WaveGenerate Nyquist Sampling Square Wave
9/12/2011
Plot Nyquist Square WavePlot Nyquist Square Wave
9/12/2011
Define Undersampled Time VectorDefine Undersampled Time Vector
9/12/2011
Generate Undersampled Square WaveGenerate Undersampled Square Wave
9/12/2011
Plot UndersampledPlot Undersampled
9/12/2011
Convolution With Linear Decay SignalConvolution With Linear Decay Signal
9/12/2011
Linear Decay SignalLinear Decay Signal
9/12/2011
Plot of ConvolutionsPlot of Convolutions
9/12/2011
Convolution with Exponential Decay SignalConvolution with Exponential Decay Signal
9/12/2011
Exponential Decay SignalExponential Decay Signal
9/12/2011
Plot of ConvolutionsPlot of Convolutions
9/12/2011
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