Cedric THIEULOT

GeoDiSP

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Example 3

In order to better understand the meaning of the output of GeoDiSP applied to a given signal, it is useful to first analyse very simple periodic signals. In what follows, the code does not use any data file, but generates the data by mmeans of their analytical expressions. Time is arbitrarily chosen to range between 0 and T=500, and discretised over N=1000 points. Then, a random perturbation is added to each time so that the samples are no more equally spaced in time.

In the terminal, run the test example as follows:

./geodisp input.test

First signal

The first signal is a simple periodic signal of period 4pi:

Hereunder are shown all the output graphs generated by GeoDiSP regarding this signal:

stats_serie1.ps
isignal_serie1.ps
rsignal_serie1.ps
nsignal_serie1.ps
both_signals_serie1.ps
lomb_transform_serie1.ps
sig95_serie1.jpg
wave_ps_sig95_serie1.ps
global_ws_serie1.ps

The frequency of the signal is the inverse of the period and is therefore approximately equal to 0.0796, the value on which the pic of the Lomb transform is centered. On the other hand, the period value, approximately equal to 12.566 is visible on the wavelet power spectrum as the horizontal yellow band, and also on the global wavelet spectrum image.

Second signal

The second signal is the sum of two simple periodic signals of periods 4pi and 20pi, of equal amplitudes:

Hereunder are shown all the output graphs generated by GeoDiSP regarding this signal:

stats_serie2.ps
isignal_serie2.ps
rsignal_serie2.ps
nsignal_serie2.ps
both_signals_serie2.ps
lomb_transform_serie2.ps
sig95_serie2.jpg
wave_ps_sig95_serie2.ps
global_ws_serie2.ps

The two frequencies present in the signal are approximately equal to 0.0796 and 0.0159, the two values on which the pics of the Lomb transform are centered. The period values, approximately equal to 12.566 and 62.832 are visible on the wavelet power spectrum as the two horizontal bands, and also on the global wavelet spectrum image.

Third signal

The third signal is composed of two different and successive periodic signals and given by:

Hereunder are shown all the output graphs generated by GeoDiSP regarding this signal:

stats_serie3.ps
isignal_serie3.ps
rsignal_serie3.ps
nsignal_serie3.ps
both_signals_serie3.ps
lomb_transform_serie3.ps
sig95_serie3.jpg
wave_ps_sig95_serie3.ps
global_ws_serie3.ps
Three different frequencies are present in the signal: 0.0159, 0.0318, and 0.0796, which are the values on which the three pics of the Lomb periodogram are centered. When looking at the wavelet power spectrum, one sees that for t < 3T/5, it shows two horizontal bands corresponding to the frequencies of the two coisines that compose the signal, and that for t > 3T/5 only one horizontal band is visible correponding to the cosine composing the signal.