[futurebasic] Re: [X-FB] Wiener Optimum Filtering

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From: Herbie Gluender <H.Gluender@...>
Date: Wed, 19 Dec 2001 12:56:50 +0100
Herbie wrote:

>... I'm not quite sure whether I would use the term tapper with respect to
>Wiener filters, because they must be tailored according to the _spectral_
>noise power that is present in the signals to be processed...

Tedd wrote:

The Wiener filter, as I knew it, was a filter for making the slopes 
of the band pass filter less susceptible to frequency problems 
(inducing higher order freq).


A further remark:

This view does not perfectly agree with what is generally accepted as a Wiener filter.

The Optimum filter proposed by Norbert Wiener is a linear filter that
reconstructs a signal that suffers from additive noise so that the sum of the
squared differences between the original undisturbed signal from the
reconstructed one in the average becomes a minimum. From this idea you may
realize the main problem with this approach. You need to know the original
signal which in most cases is unkown. So you have to estimate essentially the
power-spectrum or the autocorrelation function (both are related by Fourier
Transformation) of the original signal. Furthermore, you need to know the
power-spectrum or the autocorrelation function of the noise process which also
poses some problems because most often you only know signal plus noise...
Again you must estimate.

Most often the Wiener Optimum filter is used to correct an Inverse filter
(deconvolution) that serves the reconstruction of linearly distorted signals.
This Wiener correction mainly determines how much the Inverse filter is
allowed to amplify spectral components of the deteriorated signal in order to
maintain an optimum signal to noise ratio.

Again, there is not _one_ Wiener filter. It must be tailored according to
Wiener's definition by use of the actual signal and noise properties.

There are alternative linear approaches known as Optimum Constraint Filters.

Furthermore, one may obtain even better results by variant and/or non-linear
techniques that require even more analyses of the signal and noise situation.

**********************************
Robert wrote:

Speaking of convolution and deconvolution and such, the CIA was recently
amazed to find out that their expensive deblurred images kept coming out
looking like hotdogs.

Herbie:
True or fiction, in principle there is a lot of truth in this...
If you have sufficient and suited noise, then you can gain nearly everything
from filtering it. That's why the Wiener correction is so important!

In many cases it is worthwhile to investigate -- before any signal restoration
-- whether a desired statement can be obtained from a noisy signal, or more
precisely, with what probability this statement will be correct.
Such investigations are much more expensive than the reconstruction itself;
but what is the worth of a wrong statement, especially if it is "Hotdog".


No more apologies.

Best,

Herbie
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H.Glu@...