SIGNALS AND SYSTEMS PROBLEM SHEET 3 ECE, Exercises of Signals and Systems

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IEC222 - Signals and Systems

Problem Sheet - III

IEC222 - Signals and Systems Problem Sheet - III Let x[n] = 8[n] + 26[n —1]—-8[n-3] and An] = 28[n + 1] + 28[n - 1]. Compute and plot each of the following convolutions: (a) yila} = xn] Al] (b) y2[n] = xn + 2] * Alm] (c) y3[n] = x[n] * k[n + 2] Consider the signal re! hla] = (3) {uln + 3] — ula — 10]}. Express A and 2 in terms of # so that the following equation holds: Lyn-k-1 =< bin ay={ ASKEB , elsewhere Consider an input x[n] and a unit impulse response h[n]} given by x[n] = (3) u[n — 2], A[n] = u[n + 2]. Determine and plot the output y[7] = x[n] * A[n]. Let 1 Ofn=9 x(n] = 1, Osn=N 0, elsewhere and hln] = {3 elsewhere where N = 9 is an integer. Determine the value of N, given that y[n] = x[n]*h[n] and yl4] = 5, yl14] = 0. A linear system S has the relationship wo yle] = SS? xtklgin — 24] k=-2 between its input x[7] and its output y[”], where gl] = ulm] — u[n — 4]. (a) Determine y[n] when x{n] = 5[n — 1]. (b) Determine y[n] when x[n] = 6[n — 2]. (c) Is § LTI? (d)} Determine y[n] when x[n] = u[n]. 10. Suppose that ~ fl Osrtel x8) = { 0, elsewhere and A(t) = x(t/a), whereO