P.4: (Hayes Prob. C.7.2) (STATISTICAL DIGITAL SIGNALPROCESSING ) In this exercis
ID: 1830244 • Letter: P
Question
P.4: (Hayes Prob. C.7.2) (STATISTICAL DIGITAL SIGNALPROCESSING )In this exercise, we look at the noise cancellationproblem
considered in Example Hayes 7.2.6 (also covered in class). Let
x[n] = d[n] + g[n]
where d[n] is the harmonic process
d[n] = sin(n0 + )
with = 0.05 and is a random variable that isuniformly distributed between and
. Assume that g[n] is unit variance white noise. Suppose thata noise process v2 [n] that
is correlated with g[n] is measured by a secondary sensor. Thenoise v2 [n] is related to g[n]
by a ?ltering operation
v2 [n] = 0.8v2 [n] + g[n]
a) Using MATLAB, generate 500 samples of the processes x[n] and v2[n].
b) Derive Wiener-Hopf equations that de?ne the optimum pth-orderFIR ?lter for estimating
g[n] from v2 [n].
c) Using ?lters of order p = 2, 4 and 6, design and implement theWiener noise cancellation
ˆ
?lters. Make plots of the estimated process d[n] (noise removedsinosoid) and compare the
average squared errors for each ?lters.
d) In some situations, the desired signal may leak into thesecondary sensor. In this case
the performance of the Wiener ?lter may be severely compromised. Tosee what e?ect this
has, suppose the input to the Wiener is:
v0 [n] = v2 [n] + d[n]
where v2 [n] is the ?ltered noise de?ned above. Evaluate theperformance of the Wiener
noise canceller for several di?erent values of for ?lters oforder p = 2, 4 and 6. Comment
on your observations.
Explanation / Answer
do you have matlab at home ? problem look like you areask to filter out the noise ect ?
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