Page 110 - MATLAB Recipes for Earth Sciences

5.5 Interpolating and Analyzing Unevenly-Spaced Data 103

min(series2(:,1))
max(series2(:,1))

has a similar range from 0 to 997 kyrs. We see that both series have a mean
spacing of 3 kyrs and range from 0 to ca. 1000 kyrs. We now interpolate the
data to an evenly-spaced time axis. While doing this, we follow the rule that
number of data points should not be increased. The new time axis runs from
0 to 996 kyrs with 3 kyr intervals.
t=0 : 3 : 996;

We now interpolate the two time series to this axis with linear and spline
interpolation methods.
series1L = interp1(series1(:,1),series1(:,2),t,'linear');
series1S = interp1(series1(:,1),series1(:,2),t,'spline');
series2L = interp1(series2(:,1),series2(:,2),t,'linear');
series2S = interp1(series2(:,1),series2(:,2),t,'spline');

The results are compared by plotting the first series before and after inter-

polation.
plot(series1(:,1),series1(:,2),'ko')
hold
plot(t,series1L,'b-',t,series1S,'r-')

We already observe some significant artifacts at ca. 370 kyrs. Whereas the
linearly interpolated points are always within the range of the original data,
the spline interpolation method produces values that are unrealistically high
or low (Fig. 5.9). The results can be compared by plotting the second data
series.
plot(series2(:,1),series2(:,2),'ko')
hold
plot(t,series2L,'b-',t,series2S,'r-')
In this series, only few artifacts can be observed. We can apply the function
used above to calculate the power spectral density. We compute the FFT for
256 data points, the sampling frequency is 1/3 kyrs .
-1
[Pxx,f] = periodogram(series1L,[],256,1/3);
magnitude = abs(Pxx);

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