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Deconvolving a sampled signal?

Started by Unknown February 2, 2017
I asked for a while back about inverse filtering a high pass filtered signal to restore more of the lower frequencies.

But it would be hard to do.

But. I stumbled on to the art of deconvolution: :-)

In the beginning of my sampled data there is a known pulse that I know is a square pulse in real life (but in my sampled data it is high pass filtered).

Could I use that knowledge to deconvolve the signal to better restore the attenuated low frequencies?


On 2.2.17 12:54, karlskogasweden@gmail.com wrote:
> I asked for a while back about inverse filtering a high pass filtered signal to restore more of the lower frequencies. > > But it would be hard to do. > > But. I stumbled on to the art of deconvolution: :-) > > In the beginning of my sampled data there is a known pulse that I know is a square pulse in real life (but in my sampled data it is high pass filtered). > > Could I use that knowledge to deconvolve the signal to better restore the attenuated low frequencies?
No. What is lost is finally lost. You'd need a guessing filter, but the theory is not available yet. -- -Tauno Voipio
On Thu, 02 Feb 2017 02:54:51 -0800, karlskogasweden wrote:

> I asked for a while back about inverse filtering a high pass filtered signal to restore more of the lower frequencies. > > But it would be hard to do. > > But. I stumbled on to the art of deconvolution: :-) > > In the beginning of my sampled data there is a known pulse that I know is a square pulse in real life (but in my sampled data it is high pass filtered). > > Could I use that knowledge to deconvolve the signal to better restore the attenuated low frequencies?
It won't be _perfect_, but in most cases it should be better.
> > > > Could I use that knowledge to deconvolve the signal to better restore the attenuated low frequencies? > > It won't be _perfect_, but in most cases it should be better.
What DO you know? Do you know the characteristics of the high pass filter? Do you know the characteristics of the original signal? Is this an audio signal? m
On 02.02.2017 13:54, karlskogasweden@gmail.com wrote:
> I asked for a while back about inverse filtering a high pass filtered signal to restore more of the lower frequencies. > > But it would be hard to do. > > But. I stumbled on to the art of deconvolution: :-) > > In the beginning of my sampled data there is a known pulse that I know is a square pulse in real life (but in my sampled data it is high pass filtered). > > Could I use that knowledge to deconvolve the signal to better restore the attenuated low frequencies? >
Deconvolution is indeed an interesting, but also one of the more obscure topics. Recently I've tried to make sense of it. What I've figured out. There are various iterative approaches based on maximum-likelihood principle, somehow reminiscent of Richardson–Lucy deconvolution. One such approach is discussed there: http://mx1.kapitza.ras.ru/people/kosarev/cpc_1993.pdf And the described software can be downloaded from the "CPC Program Library": http://www.cpc.cs.qub.ac.uk/ I actually tried to download it, and there was a popup window saying that if I do, I would have to add a reference in the article I'm writing. So I thought it's kinda restrictive and didn't download the software. Although I don't think that rule is enforced, and all you have to provide is any email; so you totally can have a look. Gene
On Thu, 02 Feb 2017 02:54:51 -0800, karlskogasweden wrote:

> I asked for a while back about inverse filtering a high pass filtered > signal to restore more of the lower frequencies. > > But it would be hard to do. > > But. I stumbled on to the art of deconvolution: :-) > > In the beginning of my sampled data there is a known pulse that I know > is a square pulse in real life (but in my sampled data it is high pass > filtered). > > Could I use that knowledge to deconvolve the signal to better restore > the attenuated low frequencies?
Deconvolving is just another word for inverse filtering. The only thing that you'll get out of your filtered, known pulse is a better knowledge of the filtering that you're trying to undo. So, if the high-pass filtering isn't well known, maybe that known pulse will help. Otherwise -- not really. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com I'm looking for work -- see my website!
karlskogasweden@gmail.com wrote:
> I asked for a while back about inverse filtering a high pass filtered signal to restore more of the lower frequencies. > > But it would be hard to do. > > But. I stumbled on to the art of deconvolution: :-) > > In the beginning of my sampled data there is a known pulse that I know is a square pulse in real life (but in my sampled data it is high pass filtered). > > Could I use that knowledge to deconvolve the signal to better restore the attenuated low frequencies? > >
I would say no. I think you're up against the Second Law of thermodynamics. This being said, there may be a dither regime that will get the signal you are looking for above the noise floor. Or there may not. -- Les Cargill
Evgeny Filatov wrote:
> On 02.02.2017 13:54, karlskogasweden@gmail.com wrote: >> I asked for a while back about inverse filtering a high pass filtered >> signal to restore more of the lower frequencies. >> >> But it would be hard to do. >> >> But. I stumbled on to the art of deconvolution: :-) >> >> In the beginning of my sampled data there is a known pulse that I know >> is a square pulse in real life (but in my sampled data it is high pass >> filtered). >> >> Could I use that knowledge to deconvolve the signal to better restore >> the attenuated low frequencies? >> > > Deconvolution is indeed an interesting, but also one of the more obscure > topics. > > Recently I've tried to make sense of it. What I've figured out. There > are various iterative approaches based on maximum-likelihood principle, > somehow reminiscent of Richardson–Lucy deconvolution. > > One such approach is discussed there: > http://mx1.kapitza.ras.ru/people/kosarev/cpc_1993.pdf > > And the described software can be downloaded from the "CPC Program > Library": > http://www.cpc.cs.qub.ac.uk/ > > I actually tried to download it, and there was a popup window saying > that if I do, I would have to add a reference in the article I'm > writing. So I thought it's kinda restrictive and didn't download the > software. Although I don't think that rule is enforced, and all you have > to provide is any email; so you totally can have a look. > > Gene >
If the signals are two static vector of samples, then "take the FFT and divide" works well enough. Of course you have to have the original and post-transform signal available to make that work. -- Les Cargill
On Thursday, February 2, 2017 at 11:54:56 PM UTC+13, karlsko...@gmail.com wrote:
> I asked for a while back about inverse filtering a high pass filtered signal to restore more of the lower frequencies. > > But it would be hard to do. > > But. I stumbled on to the art of deconvolution: :-) > > In the beginning of my sampled data there is a known pulse that I know is a square pulse in real life (but in my sampled data it is high pass filtered). > > Could I use that knowledge to deconvolve the signal to better restore the attenuated low frequencies?
There are a few terms that mean teh same thing as Deconvolution. Inverse filtering and equalisation are two. Getting information back that has been lost is only one way of looking at this. If you pass data through a channel you attenuate regions you don't want to. Find the optimal inverse channel by equalisation and you have recovered that data. So the data that has been lost is still lost but you can prevent further loss by equalisation.
On Sunday, February 5, 2017 at 4:50:31 PM UTC+13, gyans...@gmail.com wrote:
> On Thursday, February 2, 2017 at 11:54:56 PM UTC+13, karlsko...@gmail.com wrote: > > I asked for a while back about inverse filtering a high pass filtered signal to restore more of the lower frequencies. > > > > But it would be hard to do. > > > > But. I stumbled on to the art of deconvolution: :-) > > > > In the beginning of my sampled data there is a known pulse that I know is a square pulse in real life (but in my sampled data it is high pass filtered). > > > > Could I use that knowledge to deconvolve the signal to better restore the attenuated low frequencies? > > There are a few terms that mean teh same thing as Deconvolution. Inverse filtering and equalisation are two. Getting information back that has been lost is only one way of looking at this. If you pass data through a channel you attenuate regions you don't want to. Find the optimal inverse channel by equalisation and you have recovered that data. So the data that has been lost is still lost but you can prevent further loss by equalisation.
There is also blind deconvolution which has been in the literature for some time now. It is related for multiple channels to de-mixing of channels. For example if you record a mixture of two sound sources in a room, the separation process is deconvolution. The secret here is to know that the original signals are statistically independent. A few now well know mathematical techniques are used based on the Kullback-Leibler Divergence property