Keren wrote:
> Hello,
> I am trying to restore a one dimentional signal using wiener deconvolution
> with a PSF. Because it's important for me to restore sharpness, but more
> important, the shape at the transient edges- the ringing is getting in my
> way.
> 
> I understand that ringing to some extent is unavoidable, but how can I
> miminize it?
> 
> Thank you,
> Keren
> 
> 

As a very general comment, ringing is caused by simultaneous sharp edges 
in both time and frequency domains.

So, if I have a "brick wall" lowpass filter and pass a step function 
through it, there will be ringing in time that is related to the inverse 
Fourier Transform of the filter / sharpness.

The way around this is to make the filter frequency response smoother. 
Even a linear taper will help quite a bit.  Making the transition band 
wider will help.  It's a matter of width and shaping to some degree.

Of course you would observe the time domain step response while tweaking 
the filter so that you get the sharpest possible time response with no 
ringing or with acceptable ringing.

Take a look at page 199 of Temes, Barcilon and Marshall "The 
Optimization of Bandlimited Sytems" Proc IEEE Vol 61 No. 2 Feb 1973 pp 
196-234.  Here, Victor Barcilon discusses time spread and frequency 
spread, deltaT and deltaOmega respectively, and shows that the Gaussian 
is optimum, that deltaT*deltaOmega>=1/2, etc......  These are optimum 
functions and not system functions.

He treats the optimum function that minimizes rise time while being
monotonic (which surely doesn't ring).

So, not to necessarily solve your problem directly, the insights might help.

Fred

Keren <kerenpur@n_o_s_p_a_m.gmail.com> wrote:

> I am trying to restore a one dimentional signal using wiener deconvolution
> with a PSF. Because it's important for me to restore sharpness, but more
> important, the shape at the transient edges- the ringing is getting in my
> way.

I don't completely understand your question, but I always recommend
Jansson's "Deconvolution of Images and Spectra" when deconvolution
problem come up.  He has a good discussion on non-linear deconvolution,
which is important in many problems.

For one example, absorption spectra data should never go below
zero, or above one.  Linear deconvolution has no such constraints,
and noise can easily cause unnatural results.  I don't remember
what he says about ringing, though.

If you are near a university library, you might be able to
find it there.

-- glen

On 08/10/2010 05:28 AM, Keren wrote:
> Hello,
> I am trying to restore a one dimentional signal using wiener deconvolution
> with a PSF. Because it's important for me to restore sharpness, but more
> important, the shape at the transient edges- the ringing is getting in my
> way.
>
> I understand that ringing to some extent is unavoidable, but how can I
> miminize it?

Do you know what generated the ringing?  If the ringing was the 
consequence of feeding a sharp edged signal into a resonance, and if 
there were no deep nulls in the original filtering, then your Wiener 
deconvolution design step should "automagically" put zeros into your 
filter that will kill the ringing mostly or alltogether.

If worse comes to worst you can twiddle the resulting filter by hand, or 
you can do a blind optimization to get the ringing out -- hopefully 
without losing too much of the rest of the signal.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

Hello,
I am trying to restore a one dimentional signal using wiener deconvolution
with a PSF. Because it's important for me to restore sharpness, but more
important, the shape at the transient edges- the ringing is getting in my
way.

I understand that ringing to some extent is unavoidable, but how can I
miminize it?

Thank you,
Keren