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PS02 - University of Illinois Spring 2011 ECE 361 Problem...

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University of Illinois Spring 2011 ECE 361: Problem Set 2 Matched and Unmatched Filtering, and Signal Design Due: Thursday February 3 at 9:30 a.m. Reading: Lecture Notes: Lectures 2-5 Throughout this Problem Set, assume that the bits being transmitted are equally likely to be 0 or 1. 1. [Matched Filtering] A communication system uses signals s 0 ( t ) and s 1 ( t ) to communicate over a white Gaussian noise channel with two-sided power spectral density N 0 / 2. The receiver is an optimum receiver (matched filter) for the signal set, and the maximum-likelihood decision rule is used. For the three sets of signals given below, compute the signal energies E 0 and E 1 , the value of h s 0 , s 1 i , and the error probability achieved by the optimum receiver. Note: You are not asked for the impulse response of the matched filter, or the sampling time T 0 , or the values of ˆ s 0 ( T 0 ) and ˆ s 1 ( T 0 ), or the variance of the noise at the receiver filter output, and you should not need any of these to find the answers to the question asked.
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