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("reading off" Fourier series coefficients for a mixture of sinusoids) Consider the periodic signal π x(t) x(t) = cos(80πt 3 (a) Find its fundamental period To and fundamental frequency fo if the unit of time is 1 mi- crosecond. = + 4 sin (90πt + Hint: The frequencies in x(t) must be integer multiples of the fundamental frequency fo in the Fourier series representation. The fundamental period To 1/fo, where fo is the largest fre- quency such that the frequencies in the mixture are integer multiples of it. (b) Specify the coefficients {X[m]} for the complex exponential Fourier series expansion ㅠ m= ∞ X[m]e¹²mfot Hint: You should be able to read these off, based on the discussion on Fourier series of real-valued signals.

("reading off" Fourier series coefficients for a mixture of sinusoids) Consider the periodic signal π x(t) x(t) = cos(80πt 3 (a) Find its fundamental period To and fundamental frequency fo if the unit of time is 1 mi- crosecond. = + 4 sin (90πt + Hint: The frequencies in x(t) must be integer multiples of the fundamental frequency fo in the Fourier series representation. The fundamental period To 1/fo, where fo is the largest fre- quency such that the frequencies in the mixture are integer multiples of it. (b) Specify the coefficients {X[m]} for the complex exponential Fourier series expansion ㅠ m= ∞ X[m]e¹²mfot Hint: You should be able to read these off, based on the discussion on Fourier series of real-valued signals.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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("reading off" Fourier series coefficients for a mixture of sinusoids) Consider the periodic signal x(t) = cos(80πt − −) + 4 sin(90πt +) - 3 3 (a) Find its fundamental period To and fundamental frequency fo if the unit of time is 1 mi- crosecond. Hint: The frequencies in x(t) must be integer multiples of the fundamental frequency fo in the Fourier series representation. The fundamental period To = 1/fo, where fo is the largest fre- quency such that the frequencies in the mixture are integer multiples of it. (b) Specify the coefficients {X[m]} for the complex exponential Fourier series expansion x(t) = Σ_X[m]ei2mmfot ∞ m=-∞ Hint: You should be able to read these off, based on the discussion on Fourier series of real-valued signals.
Transcribed Image Text:("reading off" Fourier series coefficients for a mixture of sinusoids) Consider the periodic signal x(t) = cos(80πt − −) + 4 sin(90πt +) - 3 3 (a) Find its fundamental period To and fundamental frequency fo if the unit of time is 1 mi- crosecond. Hint: The frequencies in x(t) must be integer multiples of the fundamental frequency fo in the Fourier series representation. The fundamental period To = 1/fo, where fo is the largest fre- quency such that the frequencies in the mixture are integer multiples of it. (b) Specify the coefficients {X[m]} for the complex exponential Fourier series expansion x(t) = Σ_X[m]ei2mmfot ∞ m=-∞ Hint: You should be able to read these off, based on the discussion on Fourier series of real-valued signals.
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