(1) Figure 1 is the illustration of the Fourier Transform pair in regard to a Rectangular pulse in the time domain and a Sinc function in the frequency domain. We want to observe the physical symptoms of the impact of time duration of rectangular pulse on the effective bandwidth and peak point. 72 G(f) τ 0 12 τ t (a) 1 g(t) G(f) Στ 0 -125 2t -25 0 1 Fig. 1: Fourier Transform pair: Rectangular pulse and Sinc function a) Mathematically derive the fourier transform of rectangular pulse described in Fig. 1-(a). It is in general notated as g(t) = rect(t/t) = П(t/t). Show your work in the report. b) Create the magnitude plot and phase plot of the spectra (Fourier Transform) for t = 10, 40, 70 [seconds]. In other words, overlap three magnitude curves for t = 10, 40, 70 in one plot; and overlap three phase curves for t = 10, 40, 70 in the other plot.
(1) Figure 1 is the illustration of the Fourier Transform pair in regard to a Rectangular pulse in the time domain and a Sinc function in the frequency domain. We want to observe the physical symptoms of the impact of time duration of rectangular pulse on the effective bandwidth and peak point. 72 G(f) τ 0 12 τ t (a) 1 g(t) G(f) Στ 0 -125 2t -25 0 1 Fig. 1: Fourier Transform pair: Rectangular pulse and Sinc function a) Mathematically derive the fourier transform of rectangular pulse described in Fig. 1-(a). It is in general notated as g(t) = rect(t/t) = П(t/t). Show your work in the report. b) Create the magnitude plot and phase plot of the spectra (Fourier Transform) for t = 10, 40, 70 [seconds]. In other words, overlap three magnitude curves for t = 10, 40, 70 in one plot; and overlap three phase curves for t = 10, 40, 70 in the other plot.
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...
Related questions
Question
![(1) Figure 1 is the illustration of the Fourier Transform pair in regard to a Rectangular pulse in
the time domain and a Sinc function in the frequency domain. We want to observe the physical
symptoms of the impact of time duration of rectangular pulse on the effective bandwidth and
peak point.
72
G(f)
τ
0
12
τ t
(a)
1
g(t)
G(f)
Στ
0
-125
2t
-25
0 1
Fig. 1: Fourier Transform pair: Rectangular pulse and Sinc function
a) Mathematically derive the fourier transform of rectangular pulse described in Fig. 1-(a).
It is in general notated as g(t) = rect(t/t) = П(t/t). Show your work in the report.
b) Create the magnitude plot and phase plot of the spectra (Fourier Transform) for t = 10,
40, 70 [seconds]. In other words, overlap three magnitude curves for t = 10, 40, 70
in one plot; and overlap three phase curves for t = 10, 40, 70 in the other plot.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd53b5d21-36fa-4ee2-932f-fd40dc0982c5%2Fddd261ba-9bf0-46ca-8a7d-85418739e7f5%2Fdlrq17_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(1) Figure 1 is the illustration of the Fourier Transform pair in regard to a Rectangular pulse in
the time domain and a Sinc function in the frequency domain. We want to observe the physical
symptoms of the impact of time duration of rectangular pulse on the effective bandwidth and
peak point.
72
G(f)
τ
0
12
τ t
(a)
1
g(t)
G(f)
Στ
0
-125
2t
-25
0 1
Fig. 1: Fourier Transform pair: Rectangular pulse and Sinc function
a) Mathematically derive the fourier transform of rectangular pulse described in Fig. 1-(a).
It is in general notated as g(t) = rect(t/t) = П(t/t). Show your work in the report.
b) Create the magnitude plot and phase plot of the spectra (Fourier Transform) for t = 10,
40, 70 [seconds]. In other words, overlap three magnitude curves for t = 10, 40, 70
in one plot; and overlap three phase curves for t = 10, 40, 70 in the other plot.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,