(i) Show that x(t) = el@ot is a periodic signal where wo is a constant. Also find the period of the signal. (ii) A frequency modulated signal can be represented by x(t) = A cos(wt +B sin wmt). Write an expression for the complex signal (exponential form) î (t) whose real part is x(t). (iii) Separate the periodic part of ê (t) and express it a complex Fourier series. 1 (iv) The Bessel function J, (x) is defined as :Sº ei(B sinx-nx) dx. Express x(t) in terms of summation of Bessel functions. (v) For the frequency modulated signal given in 2(b)(ii), find and sketch the frequency spectrum (with appropriate values) if B « 1.
(i) Show that x(t) = el@ot is a periodic signal where wo is a constant. Also find the period of the signal. (ii) A frequency modulated signal can be represented by x(t) = A cos(wt +B sin wmt). Write an expression for the complex signal (exponential form) î (t) whose real part is x(t). (iii) Separate the periodic part of ê (t) and express it a complex Fourier series. 1 (iv) The Bessel function J, (x) is defined as :Sº ei(B sinx-nx) dx. Express x(t) in terms of summation of Bessel functions. (v) For the frequency modulated signal given in 2(b)(ii), find and sketch the frequency spectrum (with appropriate values) if B « 1.
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
answer part (v)
![(i) Show that x(t) =
el@ot is a periodic signal where wo is a constant. Also find the period of
the signal.
(ii) A frequency modulated signal can be represented by x(t) = A cos(w.t + B sin wmt). Write
an expression for the complex signal (exponential form) î (t) whose real part is x(t).
(iii) Separate the periodic part of & (t) and express it a complex Fourier series.
(iv) The Bessel function Jn(x) is defined as ej(ß sinx-nx)
dx.
2п
Express x(t) in terms of summation of Bessel functions.
(v) For the frequency modulated signal given in 2(b)(ii), find and sketch the frequency spectrum
(with appropriate values) if ß « 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70d86970-59e6-4750-a0d7-1a72be8e9bdd%2F383c151e-5bdd-4346-bcc9-031b32d5a86c%2Fv7ladr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(i) Show that x(t) =
el@ot is a periodic signal where wo is a constant. Also find the period of
the signal.
(ii) A frequency modulated signal can be represented by x(t) = A cos(w.t + B sin wmt). Write
an expression for the complex signal (exponential form) î (t) whose real part is x(t).
(iii) Separate the periodic part of & (t) and express it a complex Fourier series.
(iv) The Bessel function Jn(x) is defined as ej(ß sinx-nx)
dx.
2п
Express x(t) in terms of summation of Bessel functions.
(v) For the frequency modulated signal given in 2(b)(ii), find and sketch the frequency spectrum
(with appropriate values) if ß « 1.
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