Answer Happy

Part Bvi Please
please provide steps with explanations so I can learn how thisis done. thank you. Use transforms only. NO integration.final answer should be an eqn in terms of sinc and cos.
5.38. An ideal lowpass digital filter has the frequency function H(2) given by H(Q) = = 1, 0≤ 2 ≤ 0, T TT < ΙΩ <π (a) Determine the unit-pulse response h[n] of the filter. (b) Compute the output response y[n] of the filter when the input x[n] is given by (i) x[n] = cos(πn/8), n = 0, ±1, ±2,... (ii) x[n] = cos(3πn/4) + cos(πn/16), n = 0, ±1, ±2,... (iii) x[n] = sinc(n/2), n = 0, ±1, ±2,… (iv) x[n] = sinc(n/4), n = 0, ±1, +2,... (v) x[n] = sinc(n/8) cos(πn/8), n = 0, ±1, ±2,... (vi) x[n] sinc(n/8) cos(πn/4), n = 0, ±1, ±2, … (c) For each signal defined in part (b), plot the input x[n] and the corresponding output y[n] to determine the effect of the filter.