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3. A discrete linear time-invariant system has an impulse response given by (0.5)-1 [n 21 h(n) n<1 0 The difference equation representation for the system is (A) y(n)0.5(n-1) (B) (n)n)+0.5y(n) у(п) — (п — 1) + 0.5y(п — 1) (D) y(n)0.5an)y(n-1) 3. Let h(n) (0.5)". From a table of z-transform pairs, 1 h'(2) 1 - 0.521 Using the shift property, since h(n) h'(n-1), H(2)= H(2) -1 Z Y(z) H(z) 1 X(z) 1 - 0.5z = 2X(2) Y(2) 0.5 Y(z)z Take the inverse z-transform of this expression у(п) - 0.5у(п — 1) %3 z(п- 1) y(n) (n- )0.5y(n- 1) The answer is (C).

3. A discrete linear time-invariant system has an impulse response given by (0.5)-1 [n 21 h(n) n<1 0 The difference equation representation for the system is (A) y(n)0.5(n-1) (B) (n)n)+0.5y(n) у(п) — (п — 1) + 0.5y(п — 1) (D) y(n)0.5an)y(n-1) 3. Let h(n) (0.5)". From a table of z-transform pairs, 1 h'(2) 1 - 0.521 Using the shift property, since h(n) h'(n-1), H(2)= H(2) -1 Z Y(z) H(z) 1 X(z) 1 - 0.5z = 2X(2) Y(2) 0.5 Y(z)z Take the inverse z-transform of this expression у(п) - 0.5у(п — 1) %3 z(п- 1) y(n) (n- )0.5y(n- 1) The answer is (C).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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3. A discrete linear time-invariant system has an impulse response given by (0.5)-1 [n 21 h(n) n<1 0 The difference equation representation for the system is (A) y(n)0.5(n-1) (B) (n)n)+0.5y(n) у(п) — (п — 1) + 0.5y(п — 1) (D) y(n)0.5an)y(n-1) 3. Let h(n) (0.5)". From a table of z-transform pairs, 1 h'(2) 1 - 0.521 Using the shift property, since h(n) h'(n-1), H(2)= H(2) -1 Z Y(z) H(z) 1 X(z) 1 - 0.5z = 2X(2) Y(2) 0.5 Y(z)z Take the inverse z-transform of this expression у(п) - 0.5у(п — 1) %3 z(п- 1) y(n) (n- )0.5y(n- 1) The answer is (C).
Transcribed Image Text:3. A discrete linear time-invariant system has an impulse response given by (0.5)-1 [n 21 h(n) n<1 0 The difference equation representation for the system is (A) y(n)0.5(n-1) (B) (n)n)+0.5y(n) у(п) — (п — 1) + 0.5y(п — 1) (D) y(n)0.5an)y(n-1) 3. Let h(n) (0.5)". From a table of z-transform pairs, 1 h'(2) 1 - 0.521 Using the shift property, since h(n) h'(n-1), H(2)= H(2) -1 Z Y(z) H(z) 1 X(z) 1 - 0.5z = 2X(2) Y(2) 0.5 Y(z)z Take the inverse z-transform of this expression у(п) - 0.5у(п — 1) %3 z(п- 1) y(n) (n- )0.5y(n- 1) The answer is (C).
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