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EEL 6502
Hmw # 3
Due Feb 8, 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 magnitude of the spectrum by 1/f (for f>0) while
keeping the phase, take the IFFT and then normalize the power to 1. Generate 5,000
samples of the pink noise to serve as input as well as the white Gaussian noise added at
the output.
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 Wiener filter to identify the unknown plant transfer function. You
can NOT use the fact that you know the plant to design the Wiener 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
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This note was uploaded on 06/05/2011 for the course EEL 6502 taught by Professor Principe during the Spring '08 term at University of Florida.
 Spring '08
 PRINCIPE

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