Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
(g) h[n] = n(=)"u[n – 1] 2.29. The following are the impulse responses of continuous-time LTI systems. Determine whether each system is causal and/or stable. Justify your answers. (a) h(t) = eu(t - 2) (b) h(t) — е 6'и (3 — 1) (c) h(t) e 2 u(t + 50)

(g) h[n] = n(=)"u[n – 1] 2.29. The following are the impulse responses of continuous-time LTI systems. Determine whether each system is causal and/or stable. Justify your answers. (a) h(t) = eu(t - 2) (b) h(t) — е 6'и (3 — 1) (c) h(t) e 2 u(t + 50)

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...
See similar textbooks
icon
Related questions
Question

Part a,b,c

### Exercise 2.29: Analyzing Impulse Responses of Continuous-Time LTI Systems The following are the impulse responses of continuous-time Linear Time-Invariant (LTI) systems. Determine whether each system is causal and/or stable. Justify your answers. #### Impulse Responses: **(a)** \( h(t) = e^{-4t}u(t - 2) \) **(b)** \( h(t) = e^{-6t}u(3 - t) \) **(c)** \( h(t) = e^{-2t}u(t + 50) \) **(d)** \( h(t) = e^{2t}u(-1 - t) \) ### Concepts for Analysis: - **Causality**: A system is causal if the output at any time depends only on values of the input at the present time and in the past. For impulse responses, this often means that the function \( h(t) \) is zero for \( t < 0 \). - **Stability**: A system is stable if its impulse response is absolutely integrable, i.e., \( \int_{-\infty}^{\infty} |h(t)| \, dt < \infty \). You are required to analyze each impulse response using these criteria and provide a justification for your conclusions.
Transcribed Image Text:### Exercise 2.29: Analyzing Impulse Responses of Continuous-Time LTI Systems The following are the impulse responses of continuous-time Linear Time-Invariant (LTI) systems. Determine whether each system is causal and/or stable. Justify your answers. #### Impulse Responses: **(a)** \( h(t) = e^{-4t}u(t - 2) \) **(b)** \( h(t) = e^{-6t}u(3 - t) \) **(c)** \( h(t) = e^{-2t}u(t + 50) \) **(d)** \( h(t) = e^{2t}u(-1 - t) \) ### Concepts for Analysis: - **Causality**: A system is causal if the output at any time depends only on values of the input at the present time and in the past. For impulse responses, this often means that the function \( h(t) \) is zero for \( t < 0 \). - **Stability**: A system is stable if its impulse response is absolutely integrable, i.e., \( \int_{-\infty}^{\infty} |h(t)| \, dt < \infty \). You are required to analyze each impulse response using these criteria and provide a justification for your conclusions.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS