1 (iv) The Bessel function J„(x) is defined as: S ei(ß sinx-nx) dx. Express x(t) in terms of summation of Bessel functions.

Introductory Circuit Analysis (13th Edition)
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Chapter1: Introduction
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answer part (iv)

(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.
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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