Geoscience Reference
In-Depth Information
updated for each individual data point, these i lters are even used in real-time
applications such as telecommunication systems. We examine this behavior
through an example in which the signal-to-noise ratio in the middle of the
time series (
x
=500) is reduced from about 10% to zero.
clear
x = 0 : 0.1 : 100; x = x';
y = sin(x);
rng(0)
yn1 = y + 0.5*randn(size(y));
yn2 = y + 0.5*randn(size(y));
yn1(501:1001) = y(501:1001);
yn2(501:1001) = y(501:1001);
plot(x,yn1,x,yn2)
h e value of
u
is again computed by
k = kron(yn1,yn1');
u = 1/max(eig(k))
which yields
u =
0.0016
We now run the adaptive i lter
canc
for 20 iterations and use the above value
of
u
.
Audio
6.2
[z,e,mer,w] = canc(yn1,yn2,0.0016,5,20);
h e plot of the mean-squared error
mer
versus the number of performed
iterations
it
with stepsize
u
plot(mer)
illustrates the performance of the adaptive i lter, although the chosen step
size
u=0.0016
clearly results in a relatively rapid convergence. Again, we can
now compare the i lter output with the original noise-free signal.
plot(x,y,'b',x,z,'r')
h is plot shows that the i lter output
y
is almost the same as the noise-free
signal
x
. h e plot
plot(x,e,'r')
shows the noise extracted from the signal. Here we can observe some signal
