A continuous-time signal x c (t), with Fourier transform X c (j) shown in Figure, is sampled

A continuous-time signal x_c(t), with Fourier transform X_c (jΩ) shown in Figure, is sampled with sampling period T = 2π / Ω₀ to form the sequence x[n] x_c(nT).

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(a) Sketch the Fourier transform X(e^jω) for |ω| < π.

(b) The signal x[n] is to be transmitted across a digital channel. At the receiver, the original signal x_c(t) must be recovered. Draw a block diagram of the recovery system and specify its characteristics. Assume that ideal filters are available.

(c) In terms of Ω₀, for what range of values of T can x_c(t) be recovered from x[n].

Transcribed Image Text:

(υ'x| -Ω0 Ω) Ωο Ω 2 2