Graphics Programs Reference
In-Depth Information
Power Spectral
Density Estimate
Power Spectral
Density Estimate
1000
7000
6000
Linear trend
800
f
1
=0.02
5000
600
4000
f
2
=0.07
3000
400
f
1
=0.02
f
2
=0.07
2000
f
3
=0.2
200
f
3
=0.2
1000
0
0
0
0.1
0.2
0.3
0.5
0
0.1
0.2
0.3
0.4
0.5
0.4
Frequency
Frequency
a
b
Fig. 5.7
Comparison of the Welch power spectra
a
of the original noisefree signal with the
periods τ
1
=50 (
f
1
=0.02), τ
2
=15 (
f
2
§0.07) and τ
3
=5 (
f
3
=0.2) and
b
the same signal overlain by
a linear trend. The linear trend is misinterpreted as a very long period with a high amplitude
by the FFT.
plot(f,magnitude,'b')
hold
[Pxx,f] = periodogram(yn,[],1024,1);
magnitude = abs(Pxx);
plot(f,magnitude,'r'), grid
xlabel('Frequency')
ylabel('Power')
title('Power Spectral Density Estimate')
Next we explore the infl uence of a linear trend on a spectrum. Long-term
trends are common features in earth science data. We will see that this trend
is misinterpreted as a very long period by the FFT. The spectrum therefore
contains a large peak with a frequency close to zero (Fig. 5.7).
yt = y + 0.005 * t;
[Pxx,f] = periodogram(y,[],1024,1);
magnitude = abs(Pxx);
[Pxxt,f] = periodogram(yt,[],1024,1);
magnitudet = abs(Pxxt);
subplot(1,2,1), plot(f,abs(Pxx))
xlabel('Frequency')
ylabel('Power')
