Compute the Fourier transform of each of the sequences in Exercise 2.1.

Exercise 2.1.

Compute the \(z\) transform of the following sequences, indicating their regions of convergence:

(a) \(x(n)=\sin (\omega n+\theta) u(n)\)

(b) \(x(n)=\cos (\omega n) u(n)\)

(c) \(x(n)= \begin{cases}n, & 0 \leq n \leq 4 \\ 0, & n<0 \text { and } n>4\end{cases}\)

(d) \(x(n)=a^{n} u(-n)\)

(e) \(x(n)=\mathrm{e}^{-\alpha n} u(n)\)

(f) \(x(n)=\mathrm{e}^{-\alpha n} \sin (\omega n) u(n)\)
(g) \(x(n)=n^{2} u(n)\).