C) please A continuous-time signal, x(t), has a Fourier transform denoted by X (w), and isexpressed as:a) (i)b)c)d)(ii)(iii)(iv)0,w²0,Write down the definition of the Fourier transform, and calculate thevalue of the integral:X (w) =(i)(ii)w<-wmif-wm ≤w wmf x(t) dtI =Using the definition of the inverse Fourier transform, calculate thevalue 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 expressionfor x(t).Determine whether energy or power provides the most suitablemeasure of the size of the time-domain signal, x(t), justifying youranswer.Find an expression for the signal, x(t), written in terms of t and trigonometricfunctions of t. Show all your working.Using the appropriate form of Parseval's theorem, calculate thevalue of the measure chosen to find the size of the signal, x(t).2x[ 2²₁² dx = ² ( ²² - ² + ²)ec²сWhat is the Nyquist frequency, wn, for the signal x(t)?The signal x(t) is now sampled at a rate of ws.+ constantIf 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.

The above question is based on the Nyquist sampling theorem which states that the minimum sampling…

Answered: A continuous-time signal, x(t), has a…

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)

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...

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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.

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