Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
Consider the causal discrete-time LTI system described by the following constant coefficient difference equation: y(n) = 1.4y(n − 1) −0.48y(n − 2) + 2x(n − 1) + x(n − 2) - (a) Determine the system function H(z) and the impulse response h(n). Is the system BIBO stable? Is the system FIR or IIR? Is the system an-all pole system? (b) Suppose the system is initially relaxed, i.e., y(−1) = 0, y(−2) = 0, and the input x(n) = n()u(n) is applied to the relaxed system. Determine the zero-state response y(n). Deter- mine the system natural response Ynr (n) and the system forced response yfr(n). Simplify your answers as much as possible.

Consider the causal discrete-time LTI system described by the following constant coefficient difference equation: y(n) = 1.4y(n − 1) −0.48y(n − 2) + 2x(n − 1) + x(n − 2) - (a) Determine the system function H(z) and the impulse response h(n). Is the system BIBO stable? Is the system FIR or IIR? Is the system an-all pole system? (b) Suppose the system is initially relaxed, i.e., y(−1) = 0, y(−2) = 0, and the input x(n) = n()u(n) is applied to the relaxed system. Determine the zero-state response y(n). Deter- mine the system natural response Ynr (n) and the system forced response yfr(n). Simplify your answers as much as possible.

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
Consider the causal discrete-time LTI system described by the following constant coefficient difference equation: \[ y(n) = 1.4y(n - 1) - 0.48y(n - 2) + 2x(n - 1) + x(n - 2) \] (a) Determine the system function \( H(z) \) and the impulse response \( h(n) \). Is the system BIBO stable? Is the system FIR or IIR? Is the system an all-pole system? (b) Suppose the system is initially relaxed, i.e., \( y(-1) = 0, y(-2) = 0 \), and the input \( x(n) = n(\frac{1}{3})^n u(n) \) is applied to the relaxed system. Determine the zero-state response \( y(n) \). Determine the system natural response \( y_{nr}(n) \) and the system forced response \( y_{fr}(n) \). Simplify your answers as much as possible.
Transcribed Image Text:Consider the causal discrete-time LTI system described by the following constant coefficient difference equation: \[ y(n) = 1.4y(n - 1) - 0.48y(n - 2) + 2x(n - 1) + x(n - 2) \] (a) Determine the system function \( H(z) \) and the impulse response \( h(n) \). Is the system BIBO stable? Is the system FIR or IIR? Is the system an all-pole system? (b) Suppose the system is initially relaxed, i.e., \( y(-1) = 0, y(-2) = 0 \), and the input \( x(n) = n(\frac{1}{3})^n u(n) \) is applied to the relaxed system. Determine the zero-state response \( y(n) \). Determine the system natural response \( y_{nr}(n) \) and the system forced response \( y_{fr}(n) \). Simplify your answers as much as possible.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Different Types of System and Its Property
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
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