Question

Signals/Systems

What do the sketches look like when justifying the answer?

(d) (20 points) Your friend, Uri Smart, manages a communications company and presents you with a schematic that implies 2(t) = f(t)b(t) where f(t) denotes the output of a hi-fidelity function generator and Uri confirms that the (double- sided) spectrum y(w) = 0 for l > π. (i) Suppose the function generator is set to f(t) = cos(Wet) with parameter ue subject to choice. Given that Uri requires the spectrum of z(t) to be zero outside the frequency band [T,5T rad/sec, choose an appropriate value of we or explain why no such value exists. Use sketches to ustifv vour answers

Answer 1

Given that z (t) = f (t) . y (t) given y (w) = 0 for Vertical-bar w Vertical-bar > pi let roughly y (w) is given f (t) = cos w c t so z (t) = cos w c t - y (t) by fourier transform z (w) = 1/2 [y (w - w c) + y (w + w c)] According to uri z (t) should be zero out side [4 pi, 5 pi] If we take w c = 5 pi then so condition is not fulfilling here . z (w) should be zero outside [4 pi, 5 pi] and it is not possible for any value of w c Because in y (w) separation is pi - (- pi) = 2 pi but we want only 5 pi - 4 pi = pi separation which is not possible because after shifting by w c, separation is still 2 pi . That's why