Zoom-frequency analysis consider the system in figure(a)

(a) Sketch the spectrum of the signal y(n) = y_R(n) + jy_l(n) if the input signal x(n) has the spectrum shown in figure(b).

(b) Suppose that we are interested in the analysis of the frequencies in the band f₀ ? f ? f₀ + ?f,?where f₀ = ?/6 and f₀ = ?/3. Determine the cutoff of a lowpass filter and the decimation factor D required to retain the information contained in this band of frequencies.

(c) Assume that, where p = 40 and f_k = k/p, k = 0, 1, . . . ., p ? 1. Compute and plot the 1024-point DFT of x(n).

(d) Repeat part (b) for the signal x(n) given in part (c) by using an appropriately designed lowpass linear phase FIR filter to determine the decimated signal s(n) = s_R(n) + js_I(n).

(e) Compute the 1024-point DFT of s(n) and investigate to see if you have obtained the expected results.

Va(n) LPF x(n) DFT y(n) eilain LPF (a) Xiu:) (b) (c) p-1 cos 2n fin 2p x(n) =