- A System Has Input X N U N And Output Y N U N 1 A Plot H Z Including Region Of Convergence B Find H N 1 (69.42 KiB) Viewed 28 times
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A system has input x[n] = ½”u[n] and output y[n] = ½”u[n−1]. a) Plot H(z), including region of convergence. b) Find h[n]. c) Find the difference equation that relates the output to the input. Solution: and Y(z) = ={i" u[n-1]}={i-1""u[n-1 = SO 1-12-¹ Y(z) 1−{z^' _‡z¯`' (1-{z^¹) _ ‡z^¹ −k2² _ }(z−4) = X(z) 1-12-¹ 1-12-¹ z(z−1) , so h[n]=8[n]+;8[n-1]-i" u[n]. 1 1-2 H(z)= The ROC is => 0.5 a) X(z): 0 -0.5 -1 +|— H(2) * -1 -0.5 0 0.5 1 -1 b) Need to divide H(z) by long division: H (2) = 1 + ½ z¯¹ 1-12 c) From H(z) in part a), y[n]− ¼ y[n−1] = }x[n−1]−}x[n-2]. O 'N -|~