Assignment:
Calculate by hand the X(Ω), DTFT of the sequence x[n]=[1 1 1 1 0 0 0 0] for n=0:7, zero else.
Using Matlab, plot the real and imaginary components of your result for X(Ω) for Ω=0:0.01:2*pi, one plot for the real, one part for the imaginary. On the same plots, use the Matlab fft and stem commands to plot the samples of X(Ω) calculated by the DFT/FFT. You code will look something like this.
n=0:0.01:2*pi;
plot(n,real(SOME_EQUATION_FOR_X(Ω?)));
hold on;
x=[1 1 1 1 0 0 0 0];
m=(0:7)*2*pi/8; % 8's the length of the sequence x[n]
stem(m,real(fft(x))); and again in a different figure for the imaginary part. The stems should fall right on the curve you plot. If not, check your result in question 2.
Provide complete and step by step solution for the question and show calculations and use formulas.