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# hmw5 - accuracy of the system identification by computing...

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EEL 6502 Hmw # 5 Due February 22, 2011 Problem I An “unknown” plant has transfer function 1 10 1 1 ) ( - - - - = z z z H and its output is added with white Gaussian noise of power N=0.1. The input to the plant is “pink” or 1/f noise . To generate 1/f noise in Matlab, the simplest way is to create white Gaussian noise with unit power, take an FFT, multiply the real part of the spectrum by 1/f (set the value for f = 0 equal to 1), normalize the power to 1 and then take the IFFT. Generate 5,000 samples of the pink noise as well as the white Gaussian noise. The user has only access to the noisy output of the plant and to its input. The goal of this problem is to design a linear filter adapted with the RLS algorithm to identify the unknown plant transfer function. You can NOT use the fact that you know the plant to design the adaptive filter, but you can use this knowledge to validate the solution obtained. Use the normalized MSE as the quality of the identification (normalize by the power of the input). I suggest that you use filters of order 5, 15 and 30. Compare the
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Unformatted text preview: accuracy of the system identification by computing the weighted error power. . )) ( ( )) ( ( log 10 * * * * --= n n WSNR T T w w w w w w Show the effect of increasing the noise N (N=0.3, 0.5) from your experiments. Explain what you observe. Compare both with the LMS and the Wiener solution. Problem II In the class website ( http://cnel.ufl.edu under classes) you will find a time series called speech 1. This file contains a spoken sentence “We were away a year ago” sampled at 10 KHz, 12 bits A/D. The purpose here is also to compare the quality of RLS predictors in this time series. The difficulty is that speech is nonstationary! Normalize the error power by the input signal power and use this measure to compare the different predictors and windows. I suggest that you use filters of order 6 and 15. Compare with both the LMS and Wiener solution....
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