Compute, using an FFT algorithm, the linear convolution of the sequences

(a) and

(b) and then

(b) and

(c) in Exercise 3.13.

Exercise 3.13.

Compute and plot the magnitude and phase of the DFT of the following finite-length sequences:

(a) \(x(n)=2 \cos \left(\pi \frac{n}{N}\right)+\sin ^{2}\left(\pi \frac{n}{N}\right)\), for \(0 \leq n \leq 10\) and \(N=11\).

(b) \(x(n)=\mathrm{e}^{-2 n}\), for \(0 \leq n \leq 20\).

(c) \(x(n)=\delta(n-1)\), for \(0 \leq n \leq 2\).

(d) \(x(n)=n\), for \(0 \leq n \leq 5\).