Geoscience Reference
In-Depth Information
shit of -0.2796 therefore equals (-0.2796.100 kyrs)/(2.ˀ)=-4.45 kyrs. h is
corresponds roughly to the phase shit of 5 kyrs introduced to the second
data series with respect to the i rst series.
h e Signal Processing Toolbox also contains a GUI function named
sptool
(for
Signal Processing Tool
), which is a more convenient tool for spectral
analysis but is not described in any detail herein.
Movie
5.1
5.6 Evolutionary Power Spectrum
h e amplitude of spectral peaks usually varies with time. h is is particularly
true for paleoclimate time series. Paleoclimate records usually show trends,
not only in the mean and variance but also in the relative contributions of
rhythmic components such as the Milankovitch cycles in marine oxygen-
isotope records. Evolutionary power spectra have the ability to map such
changes in the frequency domain. h e evolutionary or windowed power
spectrum is a modii cation of the method introduced in Section 5.3, which
computes the spectrum of overlapping segments of the time series. h ese
overlapping segments are relatively short compared to the windowed
segments used by the Welch method (Section 5.3), which is used to increase
the signal-to-noise ratio of power spectra. h e evolutionary power spectrum
method therefore uses the Short-Time Fourier Transform (STFT) instead of
the Fast Fourier Transformation (FFT). h e output from the evolutionary
power spectrum is the short-term, time-localized frequency content of the
signal. h ere are various methods to display the results. For instance, time
and frequency can be plotted on the
x
- and
y
-axes, respectively, or vice versa,
with the color of the plot being dependent on the height of the spectral peaks.
As an example we use a data set that is similar to those used in Section
5.5. h e data series contains three main periodicities of 100, 40 and 20 kyrs
and additive Gaussian noise. h e amplitudes, however, change through
time and this example can therefore be used to illustrate the advantage of
the evolutionary power spectrum method. In our example the 40 kyr cycle
appears only at er ca. 450 kyrs, whereas the 100 and 20 kyr cycles are present
throughout the time series. We i rst load from the i le
series3.txt
and display
the data (Fig. 5.11).
clear
series3 = load('series3.txt');
plot(series3(:,1),series3(:,2))
xlabel('Time (kyr)')
ylabel('d18O (permille)')
title('Signal with Varying Cyclicities')
