A long time ago someone asked on these boards why the Seti code used FFT rather than wave packet analysis for the search. Was there a good answer to this question? Wave packet analysis has a superior reputation for weak signal analysis I believe.

A long time ago someone asked on these boards why the Seti code used FFT rather than wave packet analysis for the search. Was there a good answer to this question? Wave packet analysis has a superior reputation for weak signal analysis I believe.

My response at the time, was that by my understanding, 'Wavelet Transforms' had better application with 'sparse data sets', that is where the source data is mostly zeroes. Whether or not that was a satisfactory answer is up to the OP to decide, and someone who knows more about those kindof transforms to improve on, the response I gave.

(Recalling) All my opinions from reading, of course:
Those kindof sparse datasets are, in a way, opposite to the nature of the data we're looking at here, which for the most part is random white background noise.

The other factor involved, as far as signal processing is concerned, where wavelet transform is supposed to be very useful in cases where both frequency and phase information needs preservation for certain further processing. That makes them useful for things like data compression and modulation techniques, where the problem domains have a more complex set of criteria than simply identifying the possible presence of an artifiical signal.

In that context, it's important to recognise the distinction between attempting to detect an artificial signal, and trying to decode one. So wavelet transforms for the purposes of signal detection would likely be sheer overkill, while for modulation & demodulation very handy, but not one of the scientific goals here.

Having said that, there is always room for new approaches, and those of us that grab the code and try, sometimes find valuable improvements that help the efforts, and sometimes they don't work, but in all cases it's usually a fun process, with as many (or more) approaches & techniques to try as there are people to code them.

Regards,
Jason

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"Living by the wisdom of computer science doesn't sound so bad after all. And unlike most advice, it's backed up by proofs." -- Algorithms to live by: The computer science of human decisions.

... 'Wavelet Transforms' had better application with 'sparse data sets', that is where the source data is mostly zeroes. ...

Those kindof sparse datasets are, in a way, opposite to the nature of the data we're looking at here, which for the most part is random white background noise.

... So wavelet transforms for the purposes of signal detection would likely be sheer overkill, while for modulation & demodulation very handy, but not one of the scientific goals here.

Having said that, there is always room for new approaches, ...

In that case, first question regardless of overkill or not:

Can the wavelet transform be utilised for less CPU cycles than the FFT approach for s@h?

Keep searchin',
Martin

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See new freedom: Mageia Linux
Take a look for yourself: Linux Format
The Future is what We all make IT (GPLv3)

Can the wavelet transform be utilised for less CPU cycles than the FFT approach for s@h?

IMO No, It's a different tool for a different job, But I'm not an authority on those transforms and their use either. The way is certainly clear for anyone willing to try.

This would involve rewriting the portions (majority) of the applications that are associated with familiar FFT algorithm techniques, that operate in the frequency domain, to accommodate the new wavelet representation, while still producing compatible results. [Edit: That's assuming it can be done at all, and is the right tool for the job, which is unknown to me. ]

Jason

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"Living by the wisdom of computer science doesn't sound so bad after all. And unlike most advice, it's backed up by proofs." -- Algorithms to live by: The computer science of human decisions.

Can the wavelet transform be utilised for less CPU cycles than the FFT approach for s@h?

IMO No, It's a different tool for a different job, But I'm not an authority on those transforms and their use either. The way is certainly clear for anyone willing to try.

This would involve rewriting the portions (majority) of the applications that are associated with familiar FFT algorithm techniques, that operate in the frequency domain, to accommodate the new wavelet representation, while still producing compatible results. [Edit: That's assuming it can be done at all, and is the right tool for the job, which is unknown to me. ]

Good answer even if not good for s@h.

I know that wavelets can offer phenomenal compression for certain types of images, but also with a different but equally annoying set of artefacts as with such as jpg compression...

All a case of choosing the best tool for the job?...

Use autocorrelation instead? Or is that what Astropulse is doing?

Could anything be gained by using spread-spectrum analysis to see if there is a "different texture" to the noise floor?

Or even just a crude noise energy analysis to see if any regions of the sky have a different energy distribution across frequency than what would be expected?

Keep searchin',
Martin

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See new freedom: Mageia Linux
Take a look for yourself: Linux Format
The Future is what We all make IT (GPLv3)

I know that wavelets can offer phenomenal compression for certain types of images, but also with a different but equally annoying set of artefacts as with such as jpg compression...

All a case of choosing the best tool for the job?...

That's right, since transforms are about shifting the signal representation from one domain to another, FFT to frequency domain, and wavelets to a freq/phase (coefficient subspace?) domain, uncertainty principle dictates and you get less accuracy in frequency information for that extra bit of other information.

Use autocorrelation instead? Or is that what Astropulse is doing?

I've used that method before in my school days, involved with a project tracking sunspot activity. It is useful for finding long periodic behaviour over very long data sets, and IIRC quite expensive computationally, and involves FFTs. In contrast, the fast folding algorithm used to detect repeating pulses, does not use the FFT directly, though is related, looks for repeating pulses efficiently over short time durations.

Could anything be gained by using spread-spectrum analysis to see if there is a "different texture" to the noise floor?

Or even just a crude noise energy analysis to see if any regions of the sky have a different energy distribution across frequency than what would be expected?

Keep searchin',
Martin

In effect there are Fourier analysis and fast folding processes taking place. as well as special Gaussian searches that perform a statistical fit to the kind of signal that might be expected if Arecibo drifted past a constant source, like the 'WoW signal' did.

I'm sure there could be other viable methods than used currently, and the difference between Astropulse, being a broadband analysis, and Multibeam being narrowband, each looking for several kinds of signals, indicates the scientists involved aren't necessarily assuming one particular method is better than another.

In terms of prior work, I've seen fast folding literature that dates back to 1969, and the discovery of a pulsar in the Crab nebula, as well as more modern refinement from Parkes radio observatory, and modern use of Fourier analysis techniques date back much further.

As a starting point, any 'new kind' of search would need similarly strong scientific foundations, with good reasoning as why that kind of signal / search might represent something artificial or unknown. Should someone come up with new methods, then I'm sure Berkeley would have plenty of data to make use of that.

That's certainly a bit beyond my personal scope my as volunteer/student/hourly paid instructor at a local college, but avenues for others to investigate. And they wouldn't be the first person I'm aware of to use S@H's data for alternate methods, or looking for other things than what we're looking for here.

Jason

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"Living by the wisdom of computer science doesn't sound so bad after all. And unlike most advice, it's backed up by proofs." -- Algorithms to live by: The computer science of human decisions.