Geoscience Reference
In-Depth Information
x14 = 2*sin(2*pi*t/50) + sin(2*pi*t/10) + 0.5*sin(2*pi*t/5);
plot(t,x14), axis([0 200 -4 4])
[Pxx,f] = periodogram(x14,[],1024,1);
plot(f,Pxx)
h e new Butterworth i lter is a bandstop i lter. h e stopband of the i lter is
between the frequencies 0.05 and 0.15. It can therefore be used to suppress
the period of 10, corresponding to a frequency of 0.1.
rng(0)
xn14 = x14 + randn(1,length(t));
[b14,a14] = butter(5,[0.05 0.15]/0.5,'stop');
xf14 = filtfilt(b14,a14,x14);
[Pxx,f] = periodogram(xf14,[],1024,1);
plot(f,Pxx)
figure
plot(t,xn14,'b-',t,xf14,'r-'), axis([0 200 -4 4])
h e plots show the ef ect of this i lter. h e frequency band between 0.05 and
0.15, and therefore also the frequency of 0.1, have been successfully removed
from the signal.
Audio
6.1
6.10 Adaptive Filtering
h e i xed i lters used in the previous sections make the basic assumption that
the signal degradation is known and does not change with time. However,
a priori
knowledge of the signal and noise statistical characteristics is not
usually available in most applications. In addition, both the noise level and
the variance of the genuine signal can be highly nonstationary with respect
to time, e.g., stable isotope records during a glacial-interglacial transition.
Fixed i lters cannot thus be used in a nonstationary environment without
any knowledge of the signal-to-noise ratio.
Adaptive i lters, widely used in the telecommunication industry, could
help to overcome these problems. An adaptive i lter is an inverse modeling
process that iteratively adjusts its own coei cients automatically without
requiring any
a priori
knowledge of the signal and the noise. h e operation
of an adaptive i lter includes (1) a i ltering process, the purpose of which is
to produce an output in response to a sequence of data, and (2) an adaptive
process, providing a mechanism for the adaptive control of the i lter weights
(Haykin 1991).
