Consider an lti system defined by the difference equationy[n] = —2x[n] + 4x[n — 1] — 2x[n — 2].(a) determine the impulse response of this system.(b) determine the frequency response of this system. express your answer in the formh(e j w ) = a(ejw)e—jwnd .where a[ejw) is a real function of w. explicitly specify a(ejw) and the delay nd of this system.(c) sketch a plot of the magnitude |h(ejw)| and a plot of the phase 4h() suppose that the input to the system isx 1[n] = 1 + ej0.5nn —=o< n < co. use the frequency response function to determine the corresponding output y1[n].(e) now suppose that the input to the system isx 2[n] = (1 + ej0.5nn)u[n] —ao< n < co. use the defining difference equation or discrete convolution to determine the corresponding output y2[n] for —ao < n < co. compare y1[n] and y2[n]. they should be equal for certain values of n. over what range of values of n are they equal?