Let x[n] be a periodic signal with fundamental period N and Fourier series coefficients...

Let x[n] be a periodic signal with fundamental period N and Fourier series coefficients In this problem, we derive the time-scaling property

listed in Table 3.2.

(a) Show that

(b) Show that if

Then

(c) Assuming that verify that

That is, one complex exponential in x[n] becomes a linear combination of m complex exponentials in

(d) Using the results of parts (a), (b), and (c), show that if x[n] has the Fourier coefficients