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5. A digital filter is observed to have the outputs shown here in response to a unit impulse, 6(n) yin) {0,1,2,3,0,0,0,.. x(n) 8(n) filter What is the filter's likely response to a unit pulse of three samples (e.g., x(n)= {1,1,1, 0, 0, 0, .)? (А) 0, 1, 2, 3, .. (В) 0, 1, 3, 6, .. (C) 1,1,1,0,.. 1,2, 3, 0, .. (D) 5. Obtain y(n) by convolution y(n) x(n)* f(n) Σ ( )f (π- t) k oo 0)-Σ (k)f(-k) y(0) k-oo = (0)f(0) (1)(0) = 0 (1) x(k)f(1- k) x(0)f(1)(1)f(0) (1)(1)(10) = 1 (k)f(2 k) y(2) = (0)f(2)(1)(1)(2)f(0) (1)(2)() (1)(0) 3 y(3) x(k)f(3- k) = x(0)f(3)(1)f(2)(2)f(1) = (1)(3)(1)2)(1)(1) = 6 The answer is (B).

5. A digital filter is observed to have the outputs shown here in response to a unit impulse, 6(n) yin) {0,1,2,3,0,0,0,.. x(n) 8(n) filter What is the filter's likely response to a unit pulse of three samples (e.g., x(n)= {1,1,1, 0, 0, 0, .)? (А) 0, 1, 2, 3, .. (В) 0, 1, 3, 6, .. (C) 1,1,1,0,.. 1,2, 3, 0, .. (D) 5. Obtain y(n) by convolution y(n) x(n)* f(n) Σ ( )f (π- t) k oo 0)-Σ (k)f(-k) y(0) k-oo = (0)f(0) (1)(0) = 0 (1) x(k)f(1- k) x(0)f(1)(1)f(0) (1)(1)(10) = 1 (k)f(2 k) y(2) = (0)f(2)(1)(1)(2)f(0) (1)(2)() (1)(0) 3 y(3) x(k)f(3- k) = x(0)f(3)(1)f(2)(2)f(1) = (1)(3)(1)2)(1)(1) = 6 The answer is (B).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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5. A digital filter is observed to have the outputs shown here in response to a unit impulse, 6(n) yin) {0,1,2,3,0,0,0,.. x(n) 8(n) filter What is the filter's likely response to a unit pulse of three samples (e.g., x(n)= {1,1,1, 0, 0, 0, .)? (А) 0, 1, 2, 3, .. (В) 0, 1, 3, 6, .. (C) 1,1,1,0,.. 1,2, 3, 0, .. (D)
Transcribed Image Text:5. A digital filter is observed to have the outputs shown here in response to a unit impulse, 6(n) yin) {0,1,2,3,0,0,0,.. x(n) 8(n) filter What is the filter's likely response to a unit pulse of three samples (e.g., x(n)= {1,1,1, 0, 0, 0, .)? (А) 0, 1, 2, 3, .. (В) 0, 1, 3, 6, .. (C) 1,1,1,0,.. 1,2, 3, 0, .. (D)
5. Obtain y(n) by convolution y(n) x(n)* f(n) Σ ( )f (π- t) k oo 0)-Σ (k)f(-k) y(0) k-oo = (0)f(0) (1)(0) = 0 (1) x(k)f(1- k) x(0)f(1)(1)f(0) (1)(1)(10) = 1 (k)f(2 k) y(2) = (0)f(2)(1)(1)(2)f(0) (1)(2)() (1)(0) 3 y(3) x(k)f(3- k) = x(0)f(3)(1)f(2)(2)f(1) = (1)(3)(1)2)(1)(1) = 6 The answer is (B).
Transcribed Image Text:5. Obtain y(n) by convolution y(n) x(n)* f(n) Σ ( )f (π- t) k oo 0)-Σ (k)f(-k) y(0) k-oo = (0)f(0) (1)(0) = 0 (1) x(k)f(1- k) x(0)f(1)(1)f(0) (1)(1)(10) = 1 (k)f(2 k) y(2) = (0)f(2)(1)(1)(2)f(0) (1)(2)() (1)(0) 3 y(3) x(k)f(3- k) = x(0)f(3)(1)f(2)(2)f(1) = (1)(3)(1)2)(1)(1) = 6 The answer is (B).
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