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 f lter is an optimal linear f lter that maximizes the signal-to-noise ratio of its output. The f lter’s output is an estimate of the signal. To f nd the unit-sample response of the FIR Eck- hart f 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, f nd the Eckhart f lter’s unit-sample response. (b) What is the signal-to-noise ratio produced by the Eckhart f lter? How does it compare with that produced by the corresponding Wiener f lter? (c) Now assume the signal is random, having correlation matrix . Characterize the Eckhart f 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 courses 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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This homework help was uploaded on 02/11/2008 for the course ELEC 431 taught by Professor Abercrombie during the Spring '07 term at Rice.

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