Consider a periodic function gp(·) with a period of T = 2 such that where a is a nonzero real-valued constant. (a) What are the Fourier coefficients for this function? You might find the following...

Consider a periodic function gp(·) with a period of T = 2 such that

where a is a nonzero real-valued constant.

(a) What are the Fourier coefficients for this function? You might find the following indefinite integral useful:

(b) What is the discrete power spectrum for gp(·)?

(c) Determine the mth-order Fourier series approximation gp,m(·) to gp(·).

(d) Create plots showing how well gp,m(·) approximates gp(·) for m = 2, 4, 8 and 16 when a = −1.