(3) Time-domain convolution <==> frequency-domain multiplication: an example

Random [Graphics:../Images/index_gr_54.gif] and [Graphics:../Images/index_gr_55.gif] 

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Plot [Graphics:../Images/index_gr_57.gif] and [Graphics:../Images/index_gr_58.gif]

Input sequence x[n] 
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Impulse response function h[n] 
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Frequency-domain solution

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Plot frequency representation 
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Compute inverse DTFT [Graphics:../Images/index_gr_67.gif] 
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Plot resulting time-domain sequence y[n] 
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Time-domain solution

[Graphics:../Images/index_gr_71.gif] (convolution) 
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Plot resulting time-domain sequence y[n] 
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Compute [Graphics:../Images/index_gr_75.gif] 
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Plot frequency representation 
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Show both solutions 

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Converted by Mathematica      April 16, 2003