# The derivation of the sampling theorem involves the operations of impulse train sampling and… 1 answer below »

The derivation of the sampling theorem involves the operations of impulse train sampling and reconstruction as shown in Fig. P- 12.12(a).

(a) For the input with Fourier transform depicted in Fig. P-12.12(b). use the sampling theorem to choose the sampling rate = 2π/ TS, so that x1(t) = x(t) when Plot for the value of = 2π/Ts, that is equal to the Nyquist rates

(b) If in the above system and X(jω) is as depicted above. plot the Fourier transform X,(jω) and show that aliasing occurs. There will be an infinite number of shifted copies of X (jω). so indicate the periodic pattern as a function of ω.

(c) For the conditions of part (b), determine and sketch the Fourier transform of the output X,(jω) if the frequency response of the LTI system is given by (12.78). ##### Do you need a similar assignment done for you from scratch? We have qualified writers to help you. We assure you an A+ quality paper that is free from plagiarism. Order now for an Amazing Discount! Use Discount Code "Newclient" for a 15% Discount!NB: We do not resell papers. Upon ordering, we do an original paper exclusively for you. 