Consider a periodic function

Question

Assignment:

Consider a periodic function f(x) with period L.

Over one period, f(x) = sin(2 π x/L) over the interval -L/4 to L/4, and f(x) = 0 over the intervals -L/2 to -L/4 and L/4 to L/2.

Derive an expression for the nth Fourier series coefficient, αn, in the Fourier series expansion f(x) = ∑α_n e^{i 2 π n x/L} where n is from -∞ to ∞ and α_n = 1/L * integral[f(x) * e ^{-i 2 π n x/L}]dx plot for n = -4 to 4 using matlab, and superimpose onto a plot for f(x).