What is the Fourier series expansion of the square sine wave f(x) = f(x + 2) = f

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What is the Fourier series expansion of the square sine wave f(x) = f(x + 2) = f(x) (periodic condition) Graph the first 2, 3, 4 terms of the series to see how it is converging to f(x). Also graph the frequency spectrum of f(x). Show that if we differentiate the Fourier series expansion (11.3) of the sawtooth wave term by term, we arrive at an infinite series that clearly does not represent the derivative of the sawtooth curve. Graph the frequency spectrum of the following periodic functions: f(x) = sin x f(x) = sin x + cos 2x f(x) = sin x + cos x + 0.5 sin 3x What is the Fourier transform F(xi) and the frequency spectrum C(xi) = F(xi)| of the function f(x) = Show that the absolute value of the function F(xi) = 1/(1 + ixi) is |F(xi)| = 1/(1 + xi2). First multiply the numerator and denominator by 1 - ixi to get rid of the complex number i in the denominator. Verify the orthogonality properties of sines and cosines on the interval (-L, L] sin (mpix/L) sin (npix/L) dx = cos(mpix/L) cos (npix/L) dx = sin (mpix/L) cos (npix/L) dx = 0 all m, n = 1, 2, 3,

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