Graphics Programs Reference
In-Depth Information
[Pxy,f] = cpsd(y1,y2,[],0,512,10);
phase=angle(Pxy);
plot(f,phase)
The phase shift at a frequency of
f
=0.2 (period
τ
=5) is
interp1(f,phase,0.2)
which produces the output of
ans =
1.2568
The phase spectrum is normalized to one full period
=2, therefore a phase
shift of 1.2568 equals (1.2568*5)/(2*) = 1.0001, which is again the phase
shift of one that we introduced at the beginning.
τ
5.5 Interpolating and Analyzing Unevenly-Spaced Data
Now we use our experience of evenly-spaced data to run a spectral analysis
on unevenly-spaced data. Such data are very common in earth sciences. For
example, in the fi eld of paleoceanography, the deep-sea cores are typically
sampled at constant depth intervals. Transforming evenly-spaced length-pa-
rameter data to time-parameter data in an environment with changing length-
time ratios results in unevenly-spaced time series. Numerous methods exist
for interpolating unevenly-spaced sequences of data or time series. The aim
of these
interpolation techniques
for
tx
data is to estimate the
x
-values for an
equally-spaced
t
vector from the actual irregular-spaced
tx
measurements.
Linear interpolation
is relatively simple and straightforward method for ex-
trapolating between two equally spaced data points. It predicts the
x
-values
by effectively drawing out a straight line between two neighboring measure-
ments and by calculating the appropriate point along that line. However,
the method also has its limitations. It assumes linear transitions in the data,
which introduces a number of artifacts, including the loss of high-frequency
components of the signal and limiting the data range to that of the original
measurements.
Cubic-spline interpolation
is another method for interpolating data that
are unevenly spaced. Cubic splines are piecewise continuous curves, pass-
ing through at least four data points for each step. The method has the ad-
vantage that it preserves the high-frequency information contained in the
data. However, steep gradients in the data sequence could cause spurious
