In this problem we illustrate the concepts of sampling and decimation for discretetime signals. To this end consider a signal x(n) with Fourier transform X(ω) as in Figure.

(a) Sampling x(n) with a sampling period D = 2 results to the signal. Compute and sketch the signal x_s(n) and its Fourier transform Xs(ω). Can we reconstruct x(n) from x_s(n)? How?

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

x_d(n) = x(2n)                all n

Show that X_d(ω) = Xs(ω/2). Plot the signal x_d(n) and its transform X_d(ω). Do we lose any information when we decimate the sample signal x_s(n)?

Transcribed Image Text:

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