a) The impulse response of a LTI system is given as h(t) = ße¯t cos(Nj+p)u(t); a>0. Consider h(t) to be the product of the two signals f(t) and g(t) such that h(t) = f (t)g(t) where f(t)=e*u(t) and g(t) = B cos(Q,t +g) = B cos2,(t+ Using the frequency convohtion property, or F(j0)*8(N±N,)=F(j[Q±Q,]) show that H(jN) = B- (a coso-N, sin g) +j(cosø)N (a+ jN)² +N; 1 F(jN) = a+ jN FcosD,)= πδ(Ω+Ω) + πδ(Ω-Ω,) Hint: To obtain the same result use also the time shifting property for cos(N,t + g) = cosN,(t+L). b) If H(jN)= 1-N°+ jN evahate a , B, q and N, and express h(t) using these vahes.
a) The impulse response of a LTI system is given as h(t) = ße¯t cos(Nj+p)u(t); a>0. Consider h(t) to be the product of the two signals f(t) and g(t) such that h(t) = f (t)g(t) where f(t)=e*u(t) and g(t) = B cos(Q,t +g) = B cos2,(t+ Using the frequency convohtion property, or F(j0)*8(N±N,)=F(j[Q±Q,]) show that H(jN) = B- (a coso-N, sin g) +j(cosø)N (a+ jN)² +N; 1 F(jN) = a+ jN FcosD,)= πδ(Ω+Ω) + πδ(Ω-Ω,) Hint: To obtain the same result use also the time shifting property for cos(N,t + g) = cosN,(t+L). b) If H(jN)= 1-N°+ jN evahate a , B, q and N, and express h(t) using these vahes.
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...
Related questions
Question
![Q.6
a) The impulse response of a LTI system is given as
h(t) = Beat cos(Nj+ø)u(t); a>0.
Consider h(t) to be the product of the two signals f(t) and g (t) such that
h(t)= f (t)g(t)
f(t) =e^«*u(t)
g(t) = B cos(2,t +ø) = ß cosN,(t+)
where
and
Using the frequency convohtion property, or
F(jQ)* 5(N±N,)=F(j[Q±N,]) show that
(a coso-2, sin g) + j(cos @)N
(a+ jN)² +Q;
H(jN) = B-
1
F(jN):
F{cosΩf) = πδ(Ω+Ω) + πδ(Ω -Ω,)
a+ jN
Hint: To obtain the same result use also the time shifting property for
cos (N,t + @) = cosN,(1+).
b) If
H(jN) =
1-Q² + jN
evahuate a , B, o and 2, and express h(t) using these vahes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbbccc5a-a0d3-44e4-94fe-5ee8cc924d2b%2F731d1b8c-c8d5-4852-a385-26745cc474bb%2F8st827_processed.png&w=3840&q=75)
Transcribed Image Text:Q.6
a) The impulse response of a LTI system is given as
h(t) = Beat cos(Nj+ø)u(t); a>0.
Consider h(t) to be the product of the two signals f(t) and g (t) such that
h(t)= f (t)g(t)
f(t) =e^«*u(t)
g(t) = B cos(2,t +ø) = ß cosN,(t+)
where
and
Using the frequency convohtion property, or
F(jQ)* 5(N±N,)=F(j[Q±N,]) show that
(a coso-2, sin g) + j(cos @)N
(a+ jN)² +Q;
H(jN) = B-
1
F(jN):
F{cosΩf) = πδ(Ω+Ω) + πδ(Ω -Ω,)
a+ jN
Hint: To obtain the same result use also the time shifting property for
cos (N,t + @) = cosN,(1+).
b) If
H(jN) =
1-Q² + jN
evahuate a , B, o and 2, and express h(t) using these vahes.
Transcribed Image Text:c)
Let the input to a contimuous-time LTI system with the transfer finction (fequency
response) H(jn) given in part (b) be of the form
1
4
x(t) =+-
1
cost +-cos 3t +-
25
1
cos 5t +
d)
Fill in the blanks (inchuding k) in the table bebw, showing every step of your
cakulations.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Knowledge Booster
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)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,