Exercise 4 of Assignment 2 (due 1/23/08)

Consider the function $g_p(t) = 4 \cos^6(\pi t) + \sin^2(10 \pi t)$.

a)

Show that $g_p(\cdot)$ is a periodic function, and find its Fourier representation. Hint: make use of part b of Exercise [1.3] and of the fact that the Fourier representation for a function must be unique.

b)

What is the discrete power spectrum for $g_p(\cdot)$?

c)

What is the $m$th order Fourier series approximation $g_{p,m}(\cdot)$ for this function?

d)

(Extra credit)     Create plots (similar to those in Figure 61) showing how well $g_{p,m}(\cdot)$ approximates $g_{p}(\cdot)$ for $m = 1, 2$ and $4$.

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