Solutions of the exercises

1. Spectrum S( w) (ou S(f)) of the discrete signal.

The N+1 discrete rectangular window begins for k = 0 (that is t = 0) and ends for k = N (that is t = N.D where D represents the sampling frequency). The Fourier transform is the following:

. Using the geometric serie sum with the reason a:
. In our case, the reason is .