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[Pxx,f] = periodogram(xn,[],1024,1);
plot(f,Pxx), grid
xlabel('Frequency')
ylabel('Power')
title('Auto-Spectrum')
h is spectrum now resembles a real data spectrum in the earth sciences and
the spectral peaks are set against a signii cant background noise level. h e
peak of the highest frequency even disappears into the noise and cannot be
distinguished from maxima that are attributed to noise. Both spectra can be
compared on the same plot (Fig. 5.6):
[Pxx,f] = periodogram(x,[],1024,1);
[Pxxn,f] = periodogram(xn,[],1024,1);
subplot(1,2,1)
plot(f,Pxx), grid
xlabel('Frequency')
ylabel('Power')
subplot(1,2,2)
plot(f,Pxxn), grid
xlabel('Frequency')
ylabel('Power')
Next, we explore the inl 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, producing a large peak
b
a
Fig. 5.6 Comparison of the auto-spectra for a the noise-free, and b the noisy synthetic signals
with the periods ˄ 1 =50 ( f 1 =0.02), ˄ 2 =15 ( f 2 ≈0.07) and ˄ 3 =5 ( f 3 =0.2). h e highest frequency
peak disappears completely into the background noise and cannot be distinguished from
peaks attributed to the Gaussian noise.
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