Geoscience Reference
In-Depth Information
We again use a i lled contour plot to portray the power spectrum, i.e., the
absolute value of the wavelet coei cients (Fig. 5.16 b).
contour(t,f,abs(cwtstruct.cfs),...
'LineStyle','none',...
'LineColor',[0 0 0],...
'Fill','on')
xlabel('Time')
ylabel('Frequency')
title('Wavelet Power Spectrum Using FFT Algorithm')
set(gcf,'Colormap',jet)
set(gca,'YLim',[0 0.9],...
'XGrid','On',...
'YGrid','On')
As we can see, the wavelet power spectrum derived using
cwtft
is much
smoother than that computed with
cwt
, since
cwtft
uses sinusoids to smooth
the coei cients. However, the smoothing causes a signii cant loss of detail in
the contour plot.
We now apply this concept to the synthetic data from the example to
demonstrate the windowed power spectrum method and load the synthetic
data contained in i le
series3.txt
, remembering that the data contain
periodicities of 100, 40, and 20 kyrs as well as additive Gaussian noise, and
that they are unevenly spaced about the time axis.
clear
series3 = load('series3.txt');
As for the Fourier transform and in contrast to the Lomb-Scargle algorithm,
the wavelet transform requires evenly-spaced data, and we therefore
interpolate the data using
interp1
.
t = 0 : 3 : 1000;
series3L = interp1(series3(:,1),series3(:,2),t,'linear');
Again, we i rst need to dei ne the mother wavelet and its wave number
w0
.
mother = 'morl';
w0 = 6;
We then dei ne the scales, as demonstrated in the i rst example. Unlike the
previous example the sampling interval
dt
of our time series is now 3.
dt = 3;
ds = 0.4875;
s0 = 2*dt;
nb = fix(log2(length(series3L))/ds)+1;
scales = s0*2.^((0:nb-1)*ds);
