What fraction of the energy of f is contained in the

Question

Question: The pulse train of width c is the periodic function f of period 2π given by

Suppose that f is the pulse train of width 2.

(a) What fraction of the energy of f is contained in the constant term of its Fourier series? In the constant term and the first harmonic together?

(b) How many terms of the Fourier series of f are needed to capture 90% of the energy of f?

(c) Graph f and its third Fourier approximation on the interval [-3π, 3π].