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    Matlab plots of the FFT of sequence

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    (See attached file for full problem description)

    For sequence x[n]=[1 1 1 1 0 0 0 0] for n=0:7, so N=8

    Using above x[n]:
    a) stem(x);

    b) Use the shift theorm to plot x delayed by 1, 4, 5, 6, and 8 samples, and plot the result for each. Remember the shift theorem says a delay by t0 seconds is equal to multiplying the spectrum by e-j*omega*t0. So to do this, do stem(real(ifft( exp(-j*m*t0).*fft(x)))); for the different values of t0. (the real is needed because round-off errors introduce some imaginary values that don't really exist. If you plot the imaginary part you'll see it's ~1e-15).

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    Circularity of the DFT/FFT. Using the same x[n] (shown below):
    a) stem(x);
    b) Use the shift theorm to plot x delayed by 1, 4, 5, 6, and 8 samples, and plot the result
    for each. Remember the shift theorem says a delay by t0 seconds is equal to multiplying the
    spectrum by e-jΩt0. So to do ...

    Solution Summary

    The solution is comprised of Matlab codes and plots for the FFT of the discrete sequence.

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