Question

Suppose that r(l) is a band-limited signal with the bandwidth W. Suppose that we sampled this signal with the sainpling interval T, to generate the sample sequence 1 TLI suppose that 2n/T is larger than the Nyquist rate 2W Given rn, we reconstructed a conius time signal ( using the zero-order-hold method. In other words, rr(l) n for L E [nT, (n +1)T;). In the last lecture, we derived that where s(), as usual, denotes the continuous time representation of the samples, and 1 f L E [0, T.) 0 otherwise If we consider this relation in the frequency domain, we have Nole uhat h(I)-nel (부/2). (FT) to the FT of rect(), we can show that By applying the time scaling and time delay properties of Fourier transform Now, select a correct statement (a) X-Ga) has bandwidth 2W, ie., X-Ga)-0 frw with 니 > 2W . (b) Xr(jw) has baldwidth ws + W, ie., X,(ju)-0 forw with lul > u, + W. sin(aTs/2) (c) Let x() denote the output signal of an LTI system with frequency response Hi(j) 2 when the input is zs(1). Then, Ζ 1-T,/2) is equivalent to ar(1) d) None of the above is correct

Answer 1

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