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Johathan Wehner

Feb 20, 2025

Construct the first three Fourier approximations to the square wave function

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Alycia Zemlak

Feb 20, 2025

Since f(x) is odd, it will be a pure sine series.ThenIntegral[-pi..pi] f(x)sin(nx) dx = Integral[0..pi] -2sin(nx) dx = 2/n [ cos(n*pi) – cos(n*0) ] = 2/n [ (-1)^n – 1 ]which is = 0 when n is even and = -4/n when n is odd.Since Integral[-pi..pi] sin^2(nx) dx = pi,we see that the Fourier series isf(x) = -4/(1*pi) sin(x) – 4/(3*pi) sin(3x) – 4/(5*pi) sin(5x) – …... Show More
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