Graphics Programs Reference
In-Depth Information
We now run the adaptive fi lter
canc
for 10 iterations and use the above
value of
u
.
[z,e,mer] = canc(yn1,yn2,0.0019,5,10);
The evolution of the mean-squared error
plot(mer)
illustrates the performance of the adaptive fi lter, although the chosen step
size
u=0.0019
obviously leads to a relatively fast convergence. In most ex-
amples, a smaller step size decreases the rate of convergence, but increases
the quality of the fi nal result. We therefore reduce
u
by one order of magni-
tude and run the fi lter again with more iterations.
[z,e,mer] = canc(yn1,yn2,0.0001,5,20);
The plot of the mean-squared error against the iterations
plot(mer)
now convergences after around six iterations. We now compare the fi lter
output with the original noise-free signal.
plot(x,y,'b',x,z,'r')
This plot shows that the noise level of the signal has been reduced dramati-
cally by the fi lter. Finally, the plot
plot(x,e,'r')
shows the noise extracted from the signal. In practice, the user should vary
the parameters
u
and
l
in order to obtain the optimum result.
The application of this algorithm has been demonstrated on duplicate
oxygen-isotope records from ocean sediments (Trauth 1998). The work by
Trauth (1998) illustrates the use of the modifi ed LMS algorithm, but also
another type of adaptive fi lter, the recursive least-squares (RLS) algorithm
(Haykin 1991) in various environments.
Recommended Reading
Alexander ST (1986) Adaptive signal processing: theory and applications. Springer, Berlin
Heidelberg New York
Buttkus B (2000) Spectral Analysis and Filter Theory in Applied Geophysics. Springer,
Berlin Heidelberg New York
