Use MATLAB to generate a discrete-time signal of the form: x[n]=(0.5)^n u[n], n=

Question

Use MATLAB to generate a discrete-time signal of the form: x[n]=(0.5)^n u[n], n=0,…,25

A) Plot x[n] and label figure as “Figure a”(hint: Use MATLAB function stem)

B) Plot the magnitude spectrum of the discrete time Fourier Transform of x[n] and label figure as “Figure b” (hint: Use FFT for the Fourier transform, and abs for the magnitude of the Fourier transform)

C) Plot the Phase spectrum of the discrete time Fourier Transform of x[n] and label figure as “Figure c” (hint: Use angle to find the phase of the Fourier transform)

Explanation / Answer

n = 0:1:25;
x = sqrt(n);

figure
plot(n, x);
title('Figure a');

fft_x = fft(x);

figure
plot(abs(fft_x));
title('Figure b');

figure
plot(angle(fft_x));
title('Figure c');

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