Time-Series Analysis - MATLAB Recipes for Earth Sciences - page 101

Interpolated Signals

15

10 Linearly-interpolated

data series

5

0

−5

Original data point

−10

−15 Spline-interpolated

data series

−20

−25

350 360 370 380 390 400 410 420 430 440 450

t

Fig. 5.9 Interpolation artifacts. Whereas the linearly interpolated points are always within
the range of the original data, the spline interpolation method causes unrealistic high and
low values.

Signifi cant peaks occur at frequencies of 0.01, 0.025 and 0.05 approximate-
ly, corresponding to the 100, 40 and 20 kyr cycles. Analysis of the second
time series

[Pxx,f] = periodogram(series2L,[],256,1/3);
magnitude = abs(Pxx);

plot(f,magnitude);
xlabel('Frequency')
ylabel('Power')
title('Power Spectral Density Estimate')

also yields signifi cant peaks at frequencies of 0.01, 0.025 and 0.05 (Fig. 5.10).
Now we compute the crossspectrum of both data series.

[Pxy,f] = cpsd(series1L,series2L,[],128,256,1/3);
magnitude = abs(Pxy);

plot(f,magnitude);
xlabel('Frequency')
ylabel('Power')
title('Cross PSD Estimate via Welch')

The coherence is quite convincing.

[Cxy,f] = mscohere(series1L,series2L,[],128,256,1/3);