Consider the function (a) Show that gp(·) is a periodic function, and find its Fourier representation. Hint: make use of Exercise [1.2b] and of the fact that the Fourier representation for a function...

Consider the function

(a) Show that gp(·) is a periodic function, and find its Fourier representation. Hint: make use of Exercise [1.2b] and of the fact that the Fourier representation for a function must be unique.

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

(c) What is the mth-order Fourier series approximation gp,m(·) for this function?

(d) Create plots (similar to those in Figure 51a) showing how well gp,m(·) approximates gp(·) for m = 1, 2 and 3. How well does gp,m(·) approximate gp(·) when m ≥ 4?