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Homework 8

# The noise source is an additive model of the

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Unformatted text preview: ine the transfer functions as follows: Y ( z) Y ( z) H v ( z) = H x ( z ) = . X ( z ) V ( z )=0 V ( z ) X ( z )=0 b) Evaluate these transfer functions for the special case H ( z ) = = x[n] + yv [n] where y x [n] & y v [n] are the outputs due to x[n] & v[n] , respectively. What is y v [n] in terms of v[n] ? c) (Graduate Students) Assume that v[n] is zeromean white stationary noise with variance v2 . Show that the power spectral density of the noise component of y[n] is given by: S yv yv e j = 16 v2 sin 4 ( / 2 ) y[n] = y x [n] + yv [n] 1 . Show that 1 - z -1 ( ) d) Assume that the power spectral density of x[n] is as given in the figure below. Sketch the spectral densities of the signal and noise components of y[n] = y x [n] + yv [n] and yd [n] = ydx [n] + ydv [n] . Briefly comment on the significance of your results. [Undergraduate Students: solve Part d) assuming the statements given in Parts b) and c) are correct even if you are unable to prove these statements.] v[n] H(z) H(z) x[n] y[n] z1 y[n] Ideal LPF 3. c = M S xx e j ( ) M y f [n] M y d [n] = y f [ Mn] - - M 1 EE 4541 Digital Signal...
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