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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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