Page 153 - MATLAB Recipes for Earth Sciences

6.10 Adaptive Filtering 147

range of 0 <u< l/λ where λ is the largest eigenvalue of the autocorrela-
max max
tion matrix of the reference input, leads to reasonable results (Haykin 1991)
(Fig. 6.7). The value of u is computed by

k = kron(yn1,yn1');
u = 1/max(eig(k))

which yields
u =
0.0019

Duplicate Noisy Records Learning Curve
2 0.4

1 0.3

yn 0 E 2 0.2

Mean-squared error
ï1 0.1
1st data noisy series
2nd data noisy series
ï2 0
0 5 10 15 20 0 5 10 15 20
x Iteration
a b
Filter Result Extracted Noise
2
1

1 0.8
Noise
0.6
y 0 n
0.4
ï1
0.2
Original noisefree signal
Filtered signal
ï2
0
0 5 10 15 20 0 5 10 15 20
x x
c d
Fig. 6.7 Output of the adaptive fi lter. a The duplicate records corrupted by uncorrelated noise
are fed into the adaptive filter with 5 weights with a convergence factor of 0.0019. After

10 iterations, the filter yields the b learning curve, c the noisefree record and d the noise
extracted from the duplicate records.