Suppose we have two four-point sequences x[n] and h[n] as follows: x[n] = cos (n/2). n =

Suppose we have two four-point sequences x[n] and h[n] as follows: 

x[n] = cos (πn/2).         n = 0, 1, 2, 3.

 h[n] = 2ⁿ,                    n = 0, 1, 2, 3.

(a) Calculate the four-point DFT X[k].

(b) Calculate the four-point DFT H[k].

(c) Calculate y[n] = x[n] (4) h[n] by doing the circular convolution directly.

(d) Calculate y[n] of part (c) by multiplying the DFTs of x[n] and h[n] and performing an inverse DFT.