(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]:
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).
The solution is comprised of Matlab codes and plots for the FFT of the discrete sequence.