# Hw4 - ECE 5620 Spring 2011 Homework#4 Issued Mar 2 Due Mar 18 at 5 p.m Complete all seven problems 1 Problem 2 in Chapter 9 of the text 2 Problem 3

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ECE 5620 Spring 2011 Homework #4: Issued Mar. 2, Due Mar. 18 at 5 p.m. Complete all seven problems. 1. Problem 2 in Chapter 9 of the text. 2. Problem 3 in Chapter 9 of the text. 3. Problem 4 in Chapter 9 of the text. Assume that the channel input must be nonnegative. 4. Let { Z ( t ) } t = -∞ be continuous-time Gaussian white noise with power spec- tral density S Z ( f ) = N o 2 . Suppose that { Z ( t ) } t = -∞ is passed through an ideal low-pass ﬁlter whose transfer function satisﬁes | H ( f ) | 2 = ( 1 if | f | < W 0 otherwise. Let { ˜ Z ( t ) } t = -∞ denote the output of the ﬁlter. The output is sampled at the Nyquist rate, 2 W . Show that { ˜ Z ( n 2 W ) } n = -∞ is Gaussian discrete-time white noise and deter- mine its average power. 5. Consider a discrete-time additive white Gaussian noise channel with signal- to-noise ratio S . (a) Plot the capacity as a function of S in MATLAB or an equivalent pro- gram. (b) Suppose now that the input to the channel is restricted to the two values

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## This note was uploaded on 10/03/2011 for the course ECE 5620 at Cornell University (Engineering School).

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Hw4 - ECE 5620 Spring 2011 Homework#4 Issued Mar 2 Due Mar 18 at 5 p.m Complete all seven problems 1 Problem 2 in Chapter 9 of the text 2 Problem 3

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