Forums

how to minimize ringing

Started by Keren August 10, 2010
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


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
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
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
thank you for all your help!!