Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
We have seen that the Hilbert transform introduces a 90° phase shift in the compo- nents of a signal and the transfer function of a quadrature filter can be written as e H(f) = {0 f >0 f =0. We can generalize this concept to a new transform that introduces a phase shift of 0 in the frequency components of a signal, by introducing e-je f > 0 f = 0 eje Hạ(f) = {0 f < 0 and denoting the result of this transform by xa(1), i.e., X4(f) = X(f)H9(f), where Xe(f) denotes the Fourier transform of xe (t). Throughout this problem, assume that the signal x (t) does not contain any DC components. 1. Find hø (1), the impulse response of the filter representing this transform. 2. Show that xe(t) is a linear combination of x(t) and its Hilbert transform. 3. Show that if x(t) is an energy-type signal, xe(t) will also be an energy-type signal and its energy content will be equal to the energy content of x(t).

We have seen that the Hilbert transform introduces a 90° phase shift in the compo- nents of a signal and the transfer function of a quadrature filter can be written as e H(f) = {0 f >0 f =0. We can generalize this concept to a new transform that introduces a phase shift of 0 in the frequency components of a signal, by introducing e-je f > 0 f = 0 eje Hạ(f) = {0 f < 0 and denoting the result of this transform by xa(1), i.e., X4(f) = X(f)H9(f), where Xe(f) denotes the Fourier transform of xe (t). Throughout this problem, assume that the signal x (t) does not contain any DC components. 1. Find hø (1), the impulse response of the filter representing this transform. 2. Show that xe(t) is a linear combination of x(t) and its Hilbert transform. 3. Show that if x(t) is an energy-type signal, xe(t) will also be an energy-type signal and its energy content will be equal to the energy content of x(t).

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
We have seen that the Hilbert transform introduces a 90° phase shift in the compo- nents of a signal and the transfer function of a quadrature filter can be written as e H(f) = {0 f >0 f =0. We can generalize this concept to a new transform that introduces a phase shift of 0 in the frequency components of a signal, by introducing e-je f > 0 f = 0 eje Hạ(f) = {0 f < 0 and denoting the result of this transform by xa(1), i.e., X4(f) = X(f)H9(f), where Xe(f) denotes the Fourier transform of xe (t). Throughout this problem, assume that the signal x (t) does not contain any DC components. 1. Find hø (1), the impulse response of the filter representing this transform. 2. Show that xe(t) is a linear combination of x(t) and its Hilbert transform. 3. Show that if x(t) is an energy-type signal, xe(t) will also be an energy-type signal and its energy content will be equal to the energy content of x(t).
Transcribed Image Text:We have seen that the Hilbert transform introduces a 90° phase shift in the compo- nents of a signal and the transfer function of a quadrature filter can be written as e H(f) = {0 f >0 f =0. We can generalize this concept to a new transform that introduces a phase shift of 0 in the frequency components of a signal, by introducing e-je f > 0 f = 0 eje Hạ(f) = {0 f < 0 and denoting the result of this transform by xa(1), i.e., X4(f) = X(f)H9(f), where Xe(f) denotes the Fourier transform of xe (t). Throughout this problem, assume that the signal x (t) does not contain any DC components. 1. Find hø (1), the impulse response of the filter representing this transform. 2. Show that xe(t) is a linear combination of x(t) and its Hilbert transform. 3. Show that if x(t) is an energy-type signal, xe(t) will also be an energy-type signal and its energy content will be equal to the energy content of x(t).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 8 steps with 18 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
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