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Topic: Is Match Filtering Ever Used To Recover the Signal's Original
Wave Form In Optics?

Replies: 13   Last Post: Apr 15, 2012 1:00 AM

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 BretCahill@peoplepc.com Posts: 487 Registered: 6/24/08
Re: Is Match Filtering Ever Used To Recover the Signal's Original
Wave Form In Optics?

Posted: Apr 11, 2012 11:47 PM

> >> I wasn't gonna comment any more but there is this question:
>
> >> For a matched filter you start with a replica of the signal of interest.
> >> You use this to operate on a noisy/perturbed version of the signal.

>
> >> Then you operate some more.
>
> > If you just want the magnitude of the signal multiple passes probably
> > won't be any better than one filtering.

>
> > The reason for this is the noise that was -- or maybe wasn't --
> > filtered ends up in the frequencies and phase angles of the "noise
> > free" signal altering the magnitude.

>
> > Additional passes will make the signal look more like the original
> > clean but the magnitude will always be off somewhat _even if you
> > correct for it each pass by comparing it to the magnitude of the
> > "replica" match filtered with itself_.

>
> > This could be easily demonstrated on Excel.
>
> >> Then you operate some more....
>
> >> And, in the end you get the replica which you started with????
>
> > Not if you correct for differences in the magnitude of the template
> > with the magnitude of the filtered signal.

>
> > As long as you do that each time the magnitudes will be different.
>
> > Anything more than once is probably a waste of time, however, because
> > the error will remain.

>
> >> How is that useful?
>
> > In the example shown on my page the convolution wasn't much better
> > than not filtering at all.

>
> > The additional step of recovering the original signal -- the
> > deconvolution --reduced the error from noise by 2/3rds.

>
> >> You already have the replica.  That's what you
> >> started with.  Extracting the replica from itself seems useless.

>
> > The template won't generally be the same magnitude as the match
> > filtered signal.

>
> > Bret Cahill
>
> Going beyond that..... you say that you are getting a version of the
> replica which is beyond getting the magnitude.
> I am not disputing that one bit.
> But, I still ask, what is that good for?

> Said another way:
> - if you have the replica
> - if you can extract the best estimate of magnitude with a classical
> matched filter (still subject to calibration of course)
> What is left to know?

Why do you think that the traditional match filter output will give
the same estimate of magnitude as the deconvolution of that output?

The deconvolution step reverses some of the low pass filtering effect
of match filtering so you'll get different results depending on the
noise and signal frequencies.

If you have a lot of high frequency or white noise, it may be better
to stick to traditional matched filtering, or first low pass frequency
filter and then do the matched + deconvolution filter.

In my application most of the noise will always be less than one
decade higher than the signal so the deconvolution step may always
give better results in that situation.

In the example on my page the error after the deconvolution step was
almost 2/3rds less than regular match filtering. The error was 9%
without any filtering, 8% with matched and 3% with matched +
deconvolution.

Another aspect of my application is the already high (~ 10 - 20) SNR
of the noisy signal which may be another factor to consider.

> What does further processing get you in terms of information?

> A pretty picture (i.e. waveform) that by visual inspection you can say:
> "SEE? It looks the same as what I started with!! ??

For one it eliminates a couple of inelegant steps in the square wave
binary signal recovery problem. Also the graph of the deconvolution
is a fast easy way to see how much the filter cleaned up the noise
problem.

But, to be sure, that's not the major reason.

> Try a noiseless case to make whatever point there is to this.

Without noise the accuracy of the amplitude determination will only be
limited by the number of samples in the FFT -- true for the
convolution as well as the deconvolution.

Bret Cahill