FPGA Central

Once you filter a signal, what is the best way to get the original signa
back?

Thanks..

"sauwen" <[email protected]>

> Once you filter a signal, what is the best way to get the original signal
> back?

Use a time machine.

> Thanks..

You're welcome.

--
Andrew

>"sauwen" <[email protected]>
>
>> Once you filter a signal, what is the best way to get the origina
signal
>> back?
>
>Use a time machine.
>
>> Thanks..
>
>You're welcome.
>
>--
>Andrew
>
>
>
Ha ha.. If only one exists.
Seriously, is there a way? I.e. with a simple filter?
Thanks!

>"sauwen" <[email protected]>
>
>> Once you filter a signal, what is the best way to get the origina
signal
>> back?
>
>Use a time machine.
>
>> Thanks..
>
>You're welcome.
>
>--
>Andrew
>
>
>
Ha ha.. If only one exists.
Seriously, is there a way? I.e. with a simple filter?
Thanks!

sauwen wrote:
>> "sauwen" <[email protected]>
>>
>>> Once you filter a signal, what is the best way to get the original
> signal
>>> back?
>> Use a time machine.
>>
>>> Thanks..
>> You're welcome.
>>
>> --
>> Andrew
>>
>>
>>
> Ha ha.. If only one exists.
> Seriously, is there a way? I.e. with a simple filter?
> Thanks!

There is no way to retrieve the original signal if the filter eliminates
part of the signal. If the filter merely reshaped the frequency response
without eliminating any part of it, a complementary filter can restore
the original. See preemphasis. deemphasis.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On Wed, 06 May 2009 20:25:08 -0400, Jerry Avins wrote:

> sauwen wrote:
>>> "sauwen" <[email protected]>
>>>
>>>> Once you filter a signal, what is the best way to get the original
>> signal
>>>> back?
>>> Use a time machine.
>>>
>>>> Thanks..
>>> You're welcome.
>>>
>>> --
>>> Andrew
>>>
>>>
>>>
>> Ha ha.. If only one exists.
>> Seriously, is there a way? I.e. with a simple filter? Thanks!
>
> There is no way to retrieve the original signal if the filter eliminates
> part of the signal. If the filter merely reshaped the frequency response
> without eliminating any part of it, a complementary filter can restore
> the original. See preemphasis. deemphasis.
>
I.e. if the filter has a zero at some frequency, that portion of the
signal is irretrievably lost. Worse, what you get out of a real filter
is filtered signal + a bit of noise, so where the filter attenuates the
signal a great deal you've effectively lost the original information
regardless of what a light reading of the theory may say.

--
http://www.wescottdesign.com

On May 7, 11:53*am, "sauwen" <sauwen...@gmail.com> wrote:
> Once you filter a signal, what is the best way to get the original signal
> back?
>
> Thanks..

Deconvolution is the way - at least optimal in the sense of least
squares.

Hardy

HardySpicer <[email protected]> wrote:
> On May 7, 11:53?am, "sauwen" <sauwen...@gmail.com> wrote:

>> Once you filter a signal, what is the best way to get
>> the original signal back?

> Deconvolution is the way - at least optimal in the sense
> of least squares.

Sometimes you can just invert the filter, but yes I believe
that deconvolution is better in many cases. I recommend
"Deconvolution of Images and Spectra" by Jansson, especially
for non-linear deconvolution.

-- glen

glen herrmannsfeldt wrote:
> HardySpicer <[email protected]> wrote:
>> On May 7, 11:53?am, "sauwen" <sauwen...@gmail.com> wrote:
>
>>> Once you filter a signal, what is the best way to get
>>> the original signal back?
>
>> Deconvolution is the way - at least optimal in the sense
>> of least squares.
>
> Sometimes you can just invert the filter, but yes I believe
> that deconvolution is better in many cases. I recommend
> "Deconvolution of Images and Spectra" by Jansson, especially
> for non-linear deconvolution.
>

What is the difference between deconvolution and inverse filtering ? I
thought they were the same thing (at least for linear systems) ?

Paul

On 7 Mai, 10:39, Paul Russell <pruss...@sonic.net> wrote:
> glen herrmannsfeldt wrote:
> > HardySpicer <gyansor...@gmail.com> wrote:
> >> On May 7, 11:53?am, "sauwen" <sauwen...@gmail.com> wrote:
>
> >>> Once you filter a signal, what is the best way to get
> >>> the original signal back?
>
> >> Deconvolution is the way - at least optimal in the sense
> >> of least squares.
>
> > Sometimes you can just invert the filter, but yes I believe
> > that deconvolution is better in many cases. *I recommend
> > "Deconvolution of Images and Spectra" by Jansson, especially
> > for non-linear deconvolution.
>
> What is the difference between deconvolution and inverse filtering ? I
> thought they were the same thing (at least for linear systems) ?

For all intents and purposes, 'inverse filtering; is one
of many ways to do deconvolution.

If our filter is known to you has the right properties
(all zeros and poles strictly inside the unit circle),
the inverse filer will work, except for numerical artifacts.
The ideal situation where everything works your way (filter
is known, parameters favorable) doesn't occur very often.

'Deconvloution' covers all the other cases where you
either have only crude information about the filter,
and/or the inverse filter becomes unstable.

Rune

Paul Russell <[email protected]> wrote:

> What is the difference between deconvolution and inverse filtering ? I
> thought they were the same thing (at least for linear systems) ?

Jansson mostly discusses non-linear deconvolution. He considers
the problem of absorption spectra, which must be between zero
(no absorption) and one (complete absorption). If you do linear
deconvolution on signals with noise, the result can easily go
negative or above one. Non-linear deconvolution with constraints
can, it seems, give much better results.

-- glen

Rune Allnor <[email protected]> wrote:
(snip)

> For all intents and purposes, 'inverse filtering; is one
> of many ways to do deconvolution.

> If our filter is known to you has the right properties
> (all zeros and poles strictly inside the unit circle),
> the inverse filer will work, except for numerical artifacts.
> The ideal situation where everything works your way (filter
> is known, parameters favorable) doesn't occur very often.

> 'Deconvloution' covers all the other cases where you
> either have only crude information about the filter,
> and/or the inverse filter becomes unstable.

One of the favorite examples being the original Hubble
telescope. The mirror was ground very precisely to the
wrong curve, such that the point spread function
(impulse response in DSP) was known very accurately.

For many signals, they could apply deconvolution and
correct for the distortions.

-- glen

On Thu, 7 May 2009 10:14:38 +0000 (UTC), glen herrmannsfeldt
<[email protected]> wrote:

>Rune Allnor <[email protected]> wrote:
>(snip)
>
>> For all intents and purposes, 'inverse filtering; is one
>> of many ways to do deconvolution.
>
>> If our filter is known to you has the right properties
>> (all zeros and poles strictly inside the unit circle),
>> the inverse filer will work, except for numerical artifacts.
>> The ideal situation where everything works your way (filter
>> is known, parameters favorable) doesn't occur very often.
>
>> 'Deconvloution' covers all the other cases where you
>> either have only crude information about the filter,
>> and/or the inverse filter becomes unstable.
>
>One of the favorite examples being the original Hubble
>telescope. The mirror was ground very precisely to the
>wrong curve, such that the point spread function
>(impulse response in DSP) was known very accurately.
>
>For many signals, they could apply deconvolution and
>correct for the distortions.
>
>-- glen

I thought Hubble had a spherical abberation that wasn't detected
because they skimped on the testing?

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php

Eric Jacobsen wrote:

...

> I thought Hubble had a spherical abberation that wasn't detected
> because they skimped on the testing?

The tests showed that the specified curve was accurately figured. The
very expensive test they didn't do would have shown that the spec was wrong.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On Thu, 07 May 2009 13:01:07 -0400, Jerry Avins <[email protected]> wrote:

>Eric Jacobsen wrote:
>
> ...
>
>> I thought Hubble had a spherical abberation that wasn't detected
>> because they skimped on the testing?
>
>The tests showed that the specified curve was accurately figured. The
>very expensive test they didn't do would have shown that the spec was wrong.
>
>Jerry

Ah, thanks for the clarification.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php

Eric Jacobsen <[email protected]> wrote:

> I thought Hubble had a spherical abberation that wasn't detected
> because they skimped on the testing?

It has been a while now, but I believe it was in Discover magazine
that I read the whole story. I don't think I would have described
it as "scimped on testing" but maybe. Even more, they had two
different groups each make one, and the other one was right.

At www.spacetelescope.org they call it a "malfunction of a
measuring device." I didn't find a good reference to exactly
what went wrong, though. As well as I remember it, the testing
involves another mirror at a certain distance away, and the measuring
device put it at the wrong distance. I also don't remember
if the mirror is spherical, but the difference between where
it was supposed to be and is, is (close enough to) spherical.

-- glen

glen herrmannsfeldt wrote:
> Rune Allnor <[email protected]> wrote:
> (snip)
>
>> For all intents and purposes, 'inverse filtering; is one
>> of many ways to do deconvolution.
>
>> If our filter is known to you has the right properties
>> (all zeros and poles strictly inside the unit circle),
>> the inverse filer will work, except for numerical artifacts.
>> The ideal situation where everything works your way (filter
>> is known, parameters favorable) doesn't occur very often.
>
>> 'Deconvloution' covers all the other cases where you
>> either have only crude information about the filter,
>> and/or the inverse filter becomes unstable.
>
> One of the favorite examples being the original Hubble
> telescope. The mirror was ground very precisely to the
> wrong curve, such that the point spread function
> (impulse response in DSP) was known very accurately.
>
> For many signals, they could apply deconvolution and
> correct for the distortions.
>

Thanks, both, for the clarification.

Paul