Evaluate the even and odd parts of a rectangular pulse de- fined by (-) g(t) = A rect
Evaluate the even and odd parts of a rectangular pulse de- fined by (-) g(t) = A rect
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Question
Q2.4
![T) algorithms were brought into prominence by the publication of the
- (1965). For discussions of FFT algorithms, see the books by Oppen-
1999, Ch. 9) and Haykin and Van Veen (2005). For a discussion of
y be used to perform linear filtering, see the book Numerical Recipes
02).
(a) Evaluate the even and odd parts of a rectangular pulse de-
fined by
g(t) = A rect
2
(b) What are the Fourier transforms of these two parts of the
pulse?
|G(H||
arg |G(f)||
1.0
2
-W
W
-W
W
T
2
Figure P2.4
2.4 Determine the inverse Fourier transform of the frequency
function G(f) defined by the amplitude and phase spectra shown
in Figure P2.4.
2.5 The following expression may be viewed as an approxi-
mate representation of a pulse with finite rise time:
pt + T
Tu?
du
1
g(t):
exp
where it is assumed that T >> T. Determine the Fourier transform
of g(t). What happens to this transform when we allow t to be-
come zero? Hint: Express g(t) as the superposition of two signals,
one corresponding to integration from t – T to 0, and the other
from 0 to t + T.
2.6 The Fourier transform of a signal g(t) is denoted by G(f).
Prove the following properties of the Fourier transform:
(a) If a real signal g(t) is an even function of time t, the Fourier
transform G(f) is purely real. If a real signal g(t) is an odd
function of time t the Fourier transform G(f) is purely](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81525958-071e-42c5-9778-21569535c98a%2F941ed99f-5567-4f45-a31e-f4fa356db618%2F56luwug_processed.jpeg&w=3840&q=75)
Transcribed Image Text:T) algorithms were brought into prominence by the publication of the
- (1965). For discussions of FFT algorithms, see the books by Oppen-
1999, Ch. 9) and Haykin and Van Veen (2005). For a discussion of
y be used to perform linear filtering, see the book Numerical Recipes
02).
(a) Evaluate the even and odd parts of a rectangular pulse de-
fined by
g(t) = A rect
2
(b) What are the Fourier transforms of these two parts of the
pulse?
|G(H||
arg |G(f)||
1.0
2
-W
W
-W
W
T
2
Figure P2.4
2.4 Determine the inverse Fourier transform of the frequency
function G(f) defined by the amplitude and phase spectra shown
in Figure P2.4.
2.5 The following expression may be viewed as an approxi-
mate representation of a pulse with finite rise time:
pt + T
Tu?
du
1
g(t):
exp
where it is assumed that T >> T. Determine the Fourier transform
of g(t). What happens to this transform when we allow t to be-
come zero? Hint: Express g(t) as the superposition of two signals,
one corresponding to integration from t – T to 0, and the other
from 0 to t + T.
2.6 The Fourier transform of a signal g(t) is denoted by G(f).
Prove the following properties of the Fourier transform:
(a) If a real signal g(t) is an even function of time t, the Fourier
transform G(f) is purely real. If a real signal g(t) is an odd
function of time t the Fourier transform G(f) is purely
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