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2.33. Consider a system whose input x(t) and output y(t) satisfy the first-order differential equation dy(t) dt +2y(t) = x(t). (P2.33-1) Problem 1 (3 pts each). Consider the CT system defined in textbook page 146, problem 2.33, i.e., Eq. (P2.33-1). (a) Determine the impulse response function h(t) of the system, and calculate the value of h(t) at t=0.01 (Q1), t=1 (Q2), and t=3, (Q3). (b) Determine the system output y(t) if the input signal is x(t) = e−2tu(t), and calculate the value of y(t) at t=0.01 (Q4), t=1 (Q5), and t=3, (Q6). (c) Determine the system output y(t) if the input signal is x(t) = etu(t), and calculate the value of y(t) at t=0.01 (Q7), t=1 (Q8), and t=3, (Q9). (d) Is the system memoryless? (Q10) (e) Is the system invertible? (Q11) (f) Is the system causal? (Q12) (g) Is the system stable? (Q13) (h) Is the system time-invariant? (Q14) (i) Is the system linear? (Q15)

2.33. Consider a system whose input x(t) and output y(t) satisfy the first-order differential equation dy(t) dt +2y(t) = x(t). (P2.33-1) Problem 1 (3 pts each). Consider the CT system defined in textbook page 146, problem 2.33, i.e., Eq. (P2.33-1). (a) Determine the impulse response function h(t) of the system, and calculate the value of h(t) at t=0.01 (Q1), t=1 (Q2), and t=3, (Q3). (b) Determine the system output y(t) if the input signal is x(t) = e−2tu(t), and calculate the value of y(t) at t=0.01 (Q4), t=1 (Q5), and t=3, (Q6). (c) Determine the system output y(t) if the input signal is x(t) = etu(t), and calculate the value of y(t) at t=0.01 (Q7), t=1 (Q8), and t=3, (Q9). (d) Is the system memoryless? (Q10) (e) Is the system invertible? (Q11) (f) Is the system causal? (Q12) (g) Is the system stable? (Q13) (h) Is the system time-invariant? (Q14) (i) Is the system linear? (Q15)

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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2.33. Consider a system whose input x(t) and output y(t) satisfy the first-order differential equation dy(t) dt +2y(t) = x(t). (P2.33-1)
Transcribed Image Text:2.33. Consider a system whose input x(t) and output y(t) satisfy the first-order differential equation dy(t) dt +2y(t) = x(t). (P2.33-1)
Problem 1 (3 pts each). Consider the CT system defined in textbook page 146, problem 2.33, i.e., Eq. (P2.33-1). (a) Determine the impulse response function h(t) of the system, and calculate the value of h(t) at t=0.01 (Q1), t=1 (Q2), and t=3, (Q3). (b) Determine the system output y(t) if the input signal is x(t) = e−2tu(t), and calculate the value of y(t) at t=0.01 (Q4), t=1 (Q5), and t=3, (Q6). (c) Determine the system output y(t) if the input signal is x(t) = etu(t), and calculate the value of y(t) at t=0.01 (Q7), t=1 (Q8), and t=3, (Q9). (d) Is the system memoryless? (Q10) (e) Is the system invertible? (Q11) (f) Is the system causal? (Q12) (g) Is the system stable? (Q13) (h) Is the system time-invariant? (Q14) (i) Is the system linear? (Q15)
Transcribed Image Text:Problem 1 (3 pts each). Consider the CT system defined in textbook page 146, problem 2.33, i.e., Eq. (P2.33-1). (a) Determine the impulse response function h(t) of the system, and calculate the value of h(t) at t=0.01 (Q1), t=1 (Q2), and t=3, (Q3). (b) Determine the system output y(t) if the input signal is x(t) = e−2tu(t), and calculate the value of y(t) at t=0.01 (Q4), t=1 (Q5), and t=3, (Q6). (c) Determine the system output y(t) if the input signal is x(t) = etu(t), and calculate the value of y(t) at t=0.01 (Q7), t=1 (Q8), and t=3, (Q9). (d) Is the system memoryless? (Q10) (e) Is the system invertible? (Q11) (f) Is the system causal? (Q12) (g) Is the system stable? (Q13) (h) Is the system time-invariant? (Q14) (i) Is the system linear? (Q15)
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