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Fourier Series There is a function f(t) which is given by: f(t) = sin(t/t) for 0 ≤ t ≤ 277 and f(t) = 0 for 2πT ≤t

Fourier Series There is a function f(t) which is given by: f(t) = sin(t/t) for 0 ≤ t ≤ 277 and f(t) = 0 for 2πT ≤t

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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Fourier Series There is a function f(t) which is given by: f(t) = sin(t/T) for 0 ≤ t ≤ 2πT and f(t) = 0 for 2πT ≤ t <T This function repeats periodically outside the interval [0,T) with period T (assuming that 27+ < T) a) What are the restrictions that would be expected for the Fourier coefficients aj. Which Fourier coefficient is expected to be the largest? b) Calculate the Fourier expansion, thus verifying this prediction.
Transcribed Image Text:Fourier Series There is a function f(t) which is given by: f(t) = sin(t/T) for 0 ≤ t ≤ 2πT and f(t) = 0 for 2πT ≤ t <T This function repeats periodically outside the interval [0,T) with period T (assuming that 27+ < T) a) What are the restrictions that would be expected for the Fourier coefficients aj. Which Fourier coefficient is expected to be the largest? b) Calculate the Fourier expansion, thus verifying this prediction.
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