b) Find an expression for the signal, x(t), written in terms of t and trigonometric functions of t. Show all your working. You may use the identity: 2 [ 2³² ²³² dx = e²² ( ²² - ²/1 + ² ) ₁ ecx ecr C + constant

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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B) please
Question B2
A continuous-time signal, x(t), has a Fourier transform denoted by X (w), and is
expressed as:
a)
b)
(i)
(ii)
(iii)
(iv)
0,
w<-wm
X (w) = w² if-wm ≤ w<wm
0,
w > wm
Write down the definition of the Fourier transform, and calculate the
value of the integral:
= 10x²
-∞
I =
x(t) dt
Using the definition of the inverse Fourier transform, calculate the
value of x(0); i.e. x(t) evaluated at t = 0.
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.
You may use the identity:
Using the appropriate form of Parseval's theorem, calculate the
value of the measure chosen to find the size of the signal, x(t).
Find an expression for the signal, x(t), written in terms of t and trigonometric
functions of t. Show all your working.
2
2x
2
[ 2³²0² dr = ² ( ²² - 2/2 + ²)
ecx dx ecx
C
3
+ constant
Transcribed Image Text:Question B2 A continuous-time signal, x(t), has a Fourier transform denoted by X (w), and is expressed as: a) b) (i) (ii) (iii) (iv) 0, w<-wm X (w) = w² if-wm ≤ w<wm 0, w > wm Write down the definition of the Fourier transform, and calculate the value of the integral: = 10x² -∞ I = x(t) dt Using the definition of the inverse Fourier transform, calculate the value of x(0); i.e. x(t) evaluated at t = 0. 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. You may use the identity: Using the appropriate form of Parseval's theorem, calculate the value of the measure chosen to find the size of the signal, x(t). Find an expression for the signal, x(t), written in terms of t and trigonometric functions of t. Show all your working. 2 2x 2 [ 2³²0² dr = ² ( ²² - 2/2 + ²) ecx dx ecx C 3 + constant
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