The frequency response of a desired filter hd[n] is shown in Figure P7.45. In this probl...

The frequency response of a desired filter h_d[n] is shown in Figure P7.45. In this problem, we wish to design an (M + 1)-point causal linear-phase FIR filter h[n] that minimizes the integral-squared error

where the frequency response of the filter h[n] is

and M is an even integer.

(a) Determine h_d[n].

(b) What symmetry should h[n] have in the range 0 ≤ n ≤ M? Briefly explain your reasoning.

(c) Determine h[n] in the range 0 ≤ n ≤ M.

(d) Determine an expression for the minimum integral-squared error as a function of h_d[n] and M..