In this problem we illustrate the concepts of sampling and decimation for discrete-time...

In this problem we illustrate the concepts of sampling and decimation for discrete-time signals. To this end consider a signal x(n) with Fourier transform X(ω) as in Fig. P11.5.

(a) Sampling x(n) with a sampling period D = 2 results in the signal

(b) Decimating x(n) by a factor of D = 2 produces the signal