Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
A continuous-time signal, x(t), has a Fourier transform denoted by X (w), and is expressed as: a) b) c) (i) (ii) (iii) (iv) 0, X (w) = w² 0, w<-Wm if-wm ≤ w

A continuous-time signal, x(t), has a Fourier transform denoted by X (w), and is expressed as: a) b) c) (i) (ii) (iii) (iv) 0, X (w) = w² 0, w<-Wm if-wm ≤ w

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
C) please
A continuous-time signal, x(t), has a Fourier transform denoted by X (w), and is expressed as: a) (i) b) c) d) (ii) (iii) (iv) 0, w² 0, Write down the definition of the Fourier transform, and calculate the value of the integral: X (w) = (i) (ii) w<-wm if-wm ≤w<wm w > wm f x(t) dt I = Using the definition of the inverse Fourier transform, calculate the value of x(0); i.e. x(t) evaluated at t = 0. You may use the identity: In this part of the question, you do not need to find the full expression for x(t). Determine whether energy or power provides the most suitable measure of the size of the time-domain signal, x(t), justifying your answer. Find an expression for the signal, x(t), written in terms of t and trigonometric functions of t. Show all your working. Using the appropriate form of Parseval's theorem, calculate the value of the measure chosen to find the size of the signal, x(t). 2x [ 2²₁² dx = ² ( ²² - ² + ²) ec² с What is the Nyquist frequency, wn, for the signal x(t)? The signal x(t) is now sampled at a rate of ws. + constant If we wn, plot the resulting spectrum of the sampled signal, labelling carefully key frequencies. If ws< Wn, plot the resulting spectrum of the sampled signal, explaining key characteristics of the resulting graph.
Transcribed Image Text:A continuous-time signal, x(t), has a Fourier transform denoted by X (w), and is expressed as: a) (i) b) c) d) (ii) (iii) (iv) 0, w² 0, Write down the definition of the Fourier transform, and calculate the value of the integral: X (w) = (i) (ii) w<-wm if-wm ≤w<wm w > wm f x(t) dt I = Using the definition of the inverse Fourier transform, calculate the value of x(0); i.e. x(t) evaluated at t = 0. You may use the identity: In this part of the question, you do not need to find the full expression for x(t). Determine whether energy or power provides the most suitable measure of the size of the time-domain signal, x(t), justifying your answer. Find an expression for the signal, x(t), written in terms of t and trigonometric functions of t. Show all your working. Using the appropriate form of Parseval's theorem, calculate the value of the measure chosen to find the size of the signal, x(t). 2x [ 2²₁² dx = ² ( ²² - ² + ²) ec² с What is the Nyquist frequency, wn, for the signal x(t)? The signal x(t) is now sampled at a rate of ws. + constant If we wn, plot the resulting spectrum of the sampled signal, labelling carefully key frequencies. If ws< Wn, plot the resulting spectrum of the sampled signal, explaining key characteristics of the resulting graph.
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Discrete-Time Fourier Transform (DTFT)
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