Lomb Scargle periodogram for large bandwidth signals?

[chedalb]

Dear all,

I have to deal with an unevenly sampled time history that is related to a white noise signal.

Now, I can not a priori use FFT methods as the uneven sampling is introducing artifacts that hide the real signal.
I was thinking about using Lomb Scargle processing.

Whereas the preliminary results are pretty good for single frequency component signals, I see that for my case when I turn my input signals into random the things go worse,as the amplitude of the Periodogram seems to go down proportionally with the amount of significant frequency components.

i wounder if somebody already had this issue, and has suggestion on the most adequate chain to be adopted for random signals that are also unevenly sampled.

thanks in advance for your help!
Edo

 

[IRstuff]

https://groups.google.com/forum/?fromgroups#!topic/comp.soft-sys.matlab/72nR11y1xyI

implies that it's doable, but a periodigram is intended to find a single frequency, is it not?

TTFN
faq731-376

 

[GregLocock]

"as the amplitude of the Periodogram seems to go down proportionally with the amount of significant frequency components.
"

is that not what you'd expect?


Here's what i'd do

1 synthesise some white noise with equal time sampling

1a analyse it with fft

1b analyse it with your LSSA code

1c do 1a and 1b agree?

2 extract interpolated signals from signal 1 at your uneven sampling intervals

2a analyse it with your LSSA code


2b do 2a and 1b agree well enough?


3 analyse your actual data with your LSSA code



Cheers

Greg Locock


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[chedalb]

hello

@IRstuff: as of my understanding and of the documentation I have available and is providing examples, a periodogram is able to identify more than 1 frequency component.
@GregLockck: what you indicate is the procedure I followed in order to compare and try to understand the LombScargle "animal".. and I find my self at the point of asking the community

What I understood is that
1) LombScargle is a "Power Spectrum" tool (spectrum in "units²"), whereas FFT is an "amplitude" (spectrum in "units") tool.

2) the higher the amount of spectral components (for a given constant time window and sampling), the LombScargle spectrum decreases, whereas I would expect that the amplitudes are also estimated. Therefore I understand that the spectrum restituted by the LombScargle is assessing the product spectral componenent amplitude*probability. But for this I did not find any confirmation or statement.
eg.
1 frequency component with amplitude 1-> 100% probability* amplitude 1
2 frequency components each with amplitude 1-> 50% probability* ampitude 1
3 frequency components each with amplitude 1-> 33% probability* ampitude 1
4 frequency components each with amplitude 1-> 25% probability* amplitude 1

3) What is also unclear to me is if LombScargle is a Power Spectral Density (units²/Hz) or it it "just" a Power Spectrum (units²). But in all documentation I have gone through, I don't find a clear statement ...

thanks in advance for feedbacks,
Edo

 

[IRstuff]

But, you claim you're looking at white noise...

TTFN
faq731-376

 

[chedalb]

yep. Correct, IRstuff.
and white noise is generated as a train of frequency components by creating the spectrum and then backtransforming it into the time domain and resampling it.
as stated also by GregLocock..

 

[IRstuff]

I don't read that from Greg's posting. You cannot get a "train" of frequency components, because there isn't any. Random noise is RANDOM; at any given instance, you get random parts of the PSD that randomly sum up to the random time domain signal. Pick a different window in time, and you get a different answer. You will NEVER see the PSD from any single periodogram or FFT, unless it's infinitely long. The PSD will only be as a consequence of collecting gobs of data and superimposing each individual measured spectrum and enveloping that aggregate.

TTFN
faq731-376