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Problem 2 (3 pts each). Consider the DT system described in textbook problem 2.30, page 145. (a) Determine the impulse response function h[n] of the system, and calculate the value of h[n] at n=0 (Q16), n=3 (Q17), and n=10, (Q18). (b) Determine the system output y(t) if the input signal is x[n] = 0.6" u[n], and calculate the value of y[n] at n=0 (Q19), n=3 (Q20), and n=10, (Q21). (c) Is the system memoryless? (Q22) (d) Is the system invertible? (Q23) (e) Is the system causal? (Q24) (f) Is the system stable? (Q25) (g) Is the system time-invariant? (Q26) (h) Is the system linear? (Q27) 2.30. Consider the first-order difference equation - y[n] + 2y[n 1] = x[n]. Assuming the condition of initial rest (i.e., if x[n] = 0 for n < no, then y[n] = 0 for n

Problem 2 (3 pts each). Consider the DT system described in textbook problem 2.30, page 145. (a) Determine the impulse response function h[n] of the system, and calculate the value of h[n] at n=0 (Q16), n=3 (Q17), and n=10, (Q18). (b) Determine the system output y(t) if the input signal is x[n] = 0.6" u[n], and calculate the value of y[n] at n=0 (Q19), n=3 (Q20), and n=10, (Q21). (c) Is the system memoryless? (Q22) (d) Is the system invertible? (Q23) (e) Is the system causal? (Q24) (f) Is the system stable? (Q25) (g) Is the system time-invariant? (Q26) (h) Is the system linear? (Q27) 2.30. Consider the first-order difference equation - y[n] + 2y[n 1] = x[n]. Assuming the condition of initial rest (i.e., if x[n] = 0 for n < no, then y[n] = 0 for n

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Problem 2 (3 pts each). Consider the DT system described in textbook problem 2.30, page 145. (a) Determine the impulse response function h[n] of the system, and calculate the value of h[n] at n=0 (Q16), n=3 (Q17), and n=10, (Q18). (b) Determine the system output y(t) if the input signal is x[n] = 0.6" u[n], and calculate the value of y[n] at n=0 (Q19), n=3 (Q20), and n=10, (Q21). (c) Is the system memoryless? (Q22) (d) Is the system invertible? (Q23) (e) Is the system causal? (Q24) (f) Is the system stable? (Q25) (g) Is the system time-invariant? (Q26) (h) Is the system linear? (Q27)
Transcribed Image Text:Problem 2 (3 pts each). Consider the DT system described in textbook problem 2.30, page 145. (a) Determine the impulse response function h[n] of the system, and calculate the value of h[n] at n=0 (Q16), n=3 (Q17), and n=10, (Q18). (b) Determine the system output y(t) if the input signal is x[n] = 0.6" u[n], and calculate the value of y[n] at n=0 (Q19), n=3 (Q20), and n=10, (Q21). (c) Is the system memoryless? (Q22) (d) Is the system invertible? (Q23) (e) Is the system causal? (Q24) (f) Is the system stable? (Q25) (g) Is the system time-invariant? (Q26) (h) Is the system linear? (Q27)
2.30. Consider the first-order difference equation - y[n] + 2y[n 1] = x[n]. Assuming the condition of initial rest (i.e., if x[n] = 0 for n < no, then y[n] = 0 for n<no), find the impulse response of a system whose input and output are related by this difference equation. You may solve the problem by rearranging the difference equation so as to express y[n] in terms of y[n-1] and x[n] and generating the values of y[0], y[+1], y[+2],... in that order.
Transcribed Image Text:2.30. Consider the first-order difference equation - y[n] + 2y[n 1] = x[n]. Assuming the condition of initial rest (i.e., if x[n] = 0 for n < no, then y[n] = 0 for n<no), find the impulse response of a system whose input and output are related by this difference equation. You may solve the problem by rearranging the difference equation so as to express y[n] in terms of y[n-1] and x[n] and generating the values of y[0], y[+1], y[+2],... in that order.
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