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Discrete-Time Signal Processing (2nd Edition) (Prentice-Hall Signal Processing Series)

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Electrical Engineering 431 Problem Set VII Due: March 26, 2004 7.1 Other Optimal Filters The Eckhart fi lter is an optimal linear fi lter that maximizes the signal-to-noise ratio of its output. The fi lter’s output is an estimate of the signal. To fi nd the unit-sample response of the FIR Eck- hart fi lter, consider observations of the form where the correlation matrix of the noise is known. The signal-to-noise ratio is computed according to , where is the desired unit-sample response. (a) Assuming the signal is nonrandom, fi nd the Eckhart fi lter’s unit-sample response. (b) What is the signal-to-noise ratio produced by the Eckhart fi lter? How does it compare with that produced by the corresponding Wiener fi lter? (c) Now assume the signal is random, having correlation matrix . Characterize the Eckhart fi lter. 7.2 Statistical structure and data hiding Data-hiding means sending data in such a way that it is dif
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Unformatted text preview: f cult to determine that a transmission is even present. To test your statistical analysis skills, a dataset transmission.mat located in the course’s Matlab directory contains two vectors. One, x nd , contains no transmitted data; the second, x d , contains a bit stream. These data were produced by very similar statistical models, differing only in that second included a bit stream. (a) Characterize the stochastic signal x nd as much as you can. Estimate the marginal am-plitude distribution, the correlation function, and any other statistics you think might be important. (b) Extra Credit!! Decode the bit stream by any technique you like. [ A clue : Only 128 bits are contained in this length-256 signal.] (c) What is the transmitted message?...
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