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# Matlab plots of the FFT of sequence

(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).

#### Solution Preview

Please see the attached file for detailed solution.

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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