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LOMB-Scargle Fourier Tramsform
Posted:
Jun 9, 2005 12:05 PM
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Dear list members,
I try to analyse a time series by performing the Lomb periodogram.
Unfortunately the results are not the same as the results of the
periodogram I got from the Fourier Transform for dataset with evenly
sampled data.
I used evenly sampled data to compare the results (LOMB and FOURIER) to
understand the lomb algorithm.
I have tested a devised timeseries:
time[sec] value
1 3
2 8
3 5
4 2
5 6
6 4
7 5
8 7
The mean is 5 and the variance is 4.
With a LOMB-code from http://w3eos.whoi.edu/12.747/notes/lect07/lomb.m
I have got following results:
frequency spectral density
3.5714287E-02 0.4375000
7.1428575E-02 0.4276971
0.1071429 0.4368843
0.1428571 0.4343469
0.1785714 0.4366250
0.2142857 0.4295197
0.2500000 0.4375000
0.2857143 0.4478382
0.3214286 0.4293095
0.3571429 0.4219619
0.3928572 0.4395317
0.4285715 0.4276972
0.4642858 0.4905801
0.5000001 0.4208145
0.5357143 0.4717807
0.5714286 0.4459597
Frequency is 1/((tmax-tmin)*ofac) ofac=4, hifac=1 (hifac to get the
number of frequencies)
With IDL I have got the following results:
frequency spectral density
3,57E-02 0,12898
7,14E-02 0,140956
0,1071429 0,284213
0,1428571 0,511109
0,1785714 0,813748
0,2142857 0,671165
0,25 0,312487
0,2857143 1,15578
0,3214286 2,38121
0,3571429 2,82651
0,3928572 2,33959
0,4285715 0,638402
0,4642858 0,204241
0,5000001 0,0625735
0,5357143 0,204206
0,5714286 0,638003
And at last to compare the results I have done the Fourier Transform
and that´s the results:
frequency spectral density
0,125 2,50
0,25 0,18
0,375 0,16
0,5 1,38
Frequency from 1/(N*delta_t) to 1/(2*delta_t) [nyquist]
I hoped the differences are a result of the frequencies, but IDL uses
the same as LOMB.
Can you help me to find the correct results or my mistake?
And, is the calculation of the frequencies in the LOMB algorithm
correct?
Is there a example in the internet to see how LOMB works? (best in
Fortran90)
Thanks in advance...
(Kindly excuse my english ability.)
Falk
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