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Piecewise Cubic Hermite Interpolating Polynomial and this method performs
a shape-preserving piecewise cubic interpolation. h e function avoids
the typical artifacts of the splines as it preserves the original shape of the
data series. We can apply the function used above to calculate the power
spectrum, computing the FFT for 256 data points with a sampling frequency
of 1/3 kyr -1 .
[Pxx,f] = periodogram(series1L,[],256,1/3);
plot(f,Pxx)
xlabel('Frequency')
ylabel('Power')
title('Auto-Spectrum')
Signii cant peaks occur at frequencies of approximately 0.01, 0.025 and 0.05,
corresponding approximately to the 100, 40 and 20 kyr cycles. Analysis of
the second time series
[Pxx,f] = periodogram(series2L,[],256,1/3);
plot(f,Pxx)
xlabel('Frequency')
ylabel('Power')
title('Auto-Spectrum')
also yields signii cant peaks at frequencies of 0.01, 0.025 and 0.05 (Fig. 5.10).
We now compute the cross-spectrum for both data series.
[Pxy,f] = cpsd(series1L,series2L,[],128,256,1/3);
plot(f,abs(Pxy))
xlabel('Frequency')
ylabel('Power')
title('Cross-Spectrum')
h e correlation, as indicated by the high value for the coherence, is quite
convincing.
[Cxy,f] = mscohere(series1L,series2L,[],128,256,1/3);
plot(f,Cxy)
xlabel('Frequency')
ylabel('Magnitude Squared Coherence')
title('Coherence')
We can observe a fairly high coherence at frequencies of 0.01, 0.025 and 0.05.
h e complex part of Pxy is required for calculating the phase dif erence for
each frequency.
phase = angle(Pxy);
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