Discrete-time Fourier transform (DTFT): additional illustrations

Example #1a: 1Hz cosine (finite length, discrete-time) 

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DTFT 
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Plots of DTFT 
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Plot DTFT as a function of frequency 
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Plot more than one period of the DTFT as a function of frequency 
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Example #1b: 1Hz cosine (finite length, continuous-time)

Length =  5 seconds 
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Length =  10 seconds 
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Example #1c: 1Hz cosine (longer sampling length, discrete-time)

Sampled sequence 
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DTFT 
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Plots of DTFT 
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Plot DTFT as a function of frequency 
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Example #2a: sum of cosines (homework #2, problem 7 example)

Continuous-time signal 
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Sampled sequence (fs = 10Hz) 
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DTFT 
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Plots of DTFT 
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Plot DTFT as a function of frequency 
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Plot more than one period of the DTFT as a function of frequency 
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Example #2b: infinite-length spectrum of sample waveform ([Graphics:../Images/index_gr_85.gif])

Sampling frequency 
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Original waveform 
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Continuous-time frequency spectrum (CTFT) 
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Frequency spectrum of sampled signal 
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Converted by Mathematica      March 25, 2003