IIR Gaussian Transition filters

Started by Pete Fraser September 29, 2010
Is there any software around that designs Gaussian transition
filters? ScopeIIR and Matlab both deal with most of the
Zverev standards, but neither deals with GT.

Any suggestions?

I'm looking to do 6dB and 12dB, up to 12th order,
and implementing as DF1 bi-quads.

Thanks

Pete 


On Wed, 29 Sep 2010 08:18:48 -0700, "Pete Fraser"  wrote:

>Is there any software around that designs Gaussian transition >filters? ScopeIIR and Matlab both deal with most of the >Zverev standards, but neither deals with GT.
What is the difference between a Gaussian filter and a Gaussian Transition filter? A Google search turns up only US Patent 4051458 for both "Gaussian Transition filter" and its citation, "'Filter Synthesis' by Ziev". Do you seek an analog implementation, or a digital implementation? An analog Bessel filter is an approximation to a Gaussian filter, and the approximation improves as the filter order increases. Since you asked for an IIR approximation, you could either approximate a Bessel filter by traditional means, such as step invariance (from context I suspect that step invariance will be better than impulse invariance for your application) or bilinear transform, or by nontraditional means, such as FDLS. Greg
"Greg Berchin"  wrote in message 
news:6po6a6t9fkpo6p8b68q7vrhdc6sqrerkt7@4ax.com...
> On Wed, 29 Sep 2010 08:18:48 -0700, "Pete Fraser" > wrote:
> What is the difference between a Gaussian filter and a Gaussian Transition > filter? A Google search turns up only US Patent 4051458 for both > "Gaussian > Transition filter" and its citation, "'Filter Synthesis' by Ziev".
A Gaussian transition filter is Gaussian to (typically) 6dB or 12dB down, then it falls off faster. I have used analog versions in the past. They give a reasonable compromise between a well-controlled step response, and decent stop-band attenuation. I thought it was a fairly standard term, as it's one of the standard filters given in Zverev and its derivatives (e.g., Williams).
> > Do you seek an analog implementation, or a digital implementation?
Digital.
> > An analog Bessel filter is an approximation to a Gaussian filter, and the > approximation improves as the filter order increases. > > Since you asked for an IIR approximation, you could either approximate a > Bessel > filter by traditional means, such as step invariance (from context I > suspect > that step invariance will be better than impulse invariance for your > application) or bilinear transform, or by nontraditional means, such as > FDLS.
Thanks I'll have a look at FDLS. Pete

Pete Fraser wrote:


> A Gaussian transition filter is Gaussian to (typically) 6dB or 12dB down, > then it falls off faster.
Take a Bessel filter and add a Butterworth with cutoff frequency of an octave or two higher?
> I have used analog versions in the past. They give > a reasonable compromise between a well-controlled step response, and > decent stop-band attenuation.
Engineers don't use words like "good", "well", "decent", "reasonable". Engineers use numbers. So, what do you need exactly? Linear phase approximation? Gaussian impulse response? Step response without overshoot? Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
>Pete Fraser wrote: > > >> A Gaussian transition filter is Gaussian to (typically) 6dB or 12dB
down,
>> then it falls off faster. > >Take a Bessel filter and add a Butterworth with cutoff frequency of an >octave or two higher? > >> I have used analog versions in the past. They give >> a reasonable compromise between a well-controlled step response, and >> decent stop-band attenuation.
If you want to quickly get some Bessel lowpass filters, you can use the online tool here: http://www-users.cs.york.ac.uk/~fisher/mkfilter/trad.html Nice thing of the Bessel filter approx is that the feedfordward coefficient are quite trivial to implement, and it gives you better attenuation than cascading first order allpole filters. Dave
"Vladimir Vassilevsky"  wrote in message 
news:TeqdnVXH36raHD7RnZ2dnUVZ_gadnZ2d@giganews.com...

> Take a Bessel filter and add a Butterworth with cutoff frequency of an > octave or two higher?
That sounds like a good approach. Thanks.
> Engineers don't use words like "good", "well", "decent", "reasonable".
Most engineers that I know do. You don't?
> Engineers use numbers.
I use numbers also.
> So, what do you need exactly? Linear phase approximation? Gaussian impulse > response? Step response without overshoot?
Step response with mild (~5% overshoot) but having a frequency response that has substantially better stop-band attenuation than a Gaussian (or Bessel). I'll try your combined Bessel-Butterworth approach. Pete
"gretzteam"  wrote in message 
news:T42dnZzhyOsXFz7RnZ2dnUVZ_jSdnZ2d@giganews.com...

> If you want to quickly get some Bessel lowpass filters, you can use the > online tool here: > http://www-users.cs.york.ac.uk/~fisher/mkfilter/trad.html > > Nice thing of the Bessel filter approx is that the feedfordward > coefficient > are quite trivial to implement, and it gives you better attenuation than > cascading first order allpole filters.
Thanks for the link. Pete

Pete Fraser wrote:


>>So, what do you need exactly? Linear phase approximation? Gaussian impulse >>response? Step response without overshoot? > > > Step response with mild (~5% overshoot) but having a frequency > response that has substantially better stop-band attenuation than > a Gaussian (or Bessel).
Interestingly enough, from pole-only filters of any kind, the Bessel filter of the second order has the fastest settling of the step response for the given efficient noise bandwidth.
> I'll try your combined Bessel-Butterworth approach.
Bessel-Butterworth is trivial idea; it's only merit is that it could be done as a closed form solutuon. If you need to design a filter only once, the best approach would be brute force optimization. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
On Wed, 29 Sep 2010 10:37:21 -0700, "Pete Fraser"  wrote:

>A Gaussian transition filter is Gaussian to (typically) 6dB or 12dB down, >then it falls off faster.
A true Gaussian drops off very quickly once beyond about -20 dB. For example, it changes from 20 dB attenuation to 40 dB attenuation in half an octave, and from -20 dB to -80 dB in one full octave. I'm curious as to what would require an even faster attenuation rate.
>> Do you seek an analog implementation, or a digital implementation? > >Digital.
I actually determined that from re-reading your original message, but forgot to remove that question from my response.
>Thanks I'll have a look at FDLS.
Pretty much anything that you can actually implement in analog, you can approximate pretty well in digital with FDLS. It's when you start using arbitrary magnitude and phase responses that it can fall apart. Greg
On Wed, 29 Sep 2010 10:37:21 -0700, "Pete Fraser"  wrote:

>A Gaussian transition filter is Gaussian to (typically) 6dB or 12dB down, >then it falls off faster.
A true Gaussian drops off very quickly once beyond about -20 dB. For example, it changes from 20 dB attenuation to 40 dB attenuation in half an octave, and from -20 dB to -80 dB in one full octave. I'm curious as to what would require an even faster attenuation rate.
>> Do you seek an analog implementation, or a digital implementation? > >Digital.
I actually determined that from re-reading your original message, but forgot to remove that question from my response.
>Thanks I'll have a look at FDLS.
Pretty much anything that you can actually implement in analog, you can approximate pretty well in digital with FDLS. It's when you start using arbitrary magnitude and phase responses that it can fall apart. Greg

Pete Fraser wrote:


>>So, what do you need exactly? Linear phase approximation? Gaussian impulse >>response? Step response without overshoot? > > > Step response with mild (~5% overshoot) but having a frequency > response that has substantially better stop-band attenuation than > a Gaussian (or Bessel).
Interestingly enough, from pole-only filters of any kind, the Bessel filter of the second order has the fastest settling of the step response for the given efficient noise bandwidth.
> I'll try your combined Bessel-Butterworth approach.
Bessel-Butterworth is trivial idea; it's only merit is that it could be done as a closed form solutuon. If you need to design a filter only once, the best approach would be brute force optimization. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
"gretzteam"  wrote in message 
news:T42dnZzhyOsXFz7RnZ2dnUVZ_jSdnZ2d@giganews.com...

> If you want to quickly get some Bessel lowpass filters, you can use the > online tool here: > http://www-users.cs.york.ac.uk/~fisher/mkfilter/trad.html > > Nice thing of the Bessel filter approx is that the feedfordward > coefficient > are quite trivial to implement, and it gives you better attenuation than > cascading first order allpole filters.
Thanks for the link. Pete
"Vladimir Vassilevsky"  wrote in message 
news:TeqdnVXH36raHD7RnZ2dnUVZ_gadnZ2d@giganews.com...

> Take a Bessel filter and add a Butterworth with cutoff frequency of an > octave or two higher?
That sounds like a good approach. Thanks.
> Engineers don't use words like "good", "well", "decent", "reasonable".
Most engineers that I know do. You don't?
> Engineers use numbers.
I use numbers also.
> So, what do you need exactly? Linear phase approximation? Gaussian impulse > response? Step response without overshoot?
Step response with mild (~5% overshoot) but having a frequency response that has substantially better stop-band attenuation than a Gaussian (or Bessel). I'll try your combined Bessel-Butterworth approach. Pete
>Pete Fraser wrote: > > >> A Gaussian transition filter is Gaussian to (typically) 6dB or 12dB
down,
>> then it falls off faster. > >Take a Bessel filter and add a Butterworth with cutoff frequency of an >octave or two higher? > >> I have used analog versions in the past. They give >> a reasonable compromise between a well-controlled step response, and >> decent stop-band attenuation.
If you want to quickly get some Bessel lowpass filters, you can use the online tool here: http://www-users.cs.york.ac.uk/~fisher/mkfilter/trad.html Nice thing of the Bessel filter approx is that the feedfordward coefficient are quite trivial to implement, and it gives you better attenuation than cascading first order allpole filters. Dave

Pete Fraser wrote:


> A Gaussian transition filter is Gaussian to (typically) 6dB or 12dB down, > then it falls off faster.
Take a Bessel filter and add a Butterworth with cutoff frequency of an octave or two higher?
> I have used analog versions in the past. They give > a reasonable compromise between a well-controlled step response, and > decent stop-band attenuation.
Engineers don't use words like "good", "well", "decent", "reasonable". Engineers use numbers. So, what do you need exactly? Linear phase approximation? Gaussian impulse response? Step response without overshoot? Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
"Greg Berchin"  wrote in message 
news:6po6a6t9fkpo6p8b68q7vrhdc6sqrerkt7@4ax.com...
> On Wed, 29 Sep 2010 08:18:48 -0700, "Pete Fraser" > wrote:
> What is the difference between a Gaussian filter and a Gaussian Transition > filter? A Google search turns up only US Patent 4051458 for both > "Gaussian > Transition filter" and its citation, "'Filter Synthesis' by Ziev".
A Gaussian transition filter is Gaussian to (typically) 6dB or 12dB down, then it falls off faster. I have used analog versions in the past. They give a reasonable compromise between a well-controlled step response, and decent stop-band attenuation. I thought it was a fairly standard term, as it's one of the standard filters given in Zverev and its derivatives (e.g., Williams).
> > Do you seek an analog implementation, or a digital implementation?
Digital.
> > An analog Bessel filter is an approximation to a Gaussian filter, and the > approximation improves as the filter order increases. > > Since you asked for an IIR approximation, you could either approximate a > Bessel > filter by traditional means, such as step invariance (from context I > suspect > that step invariance will be better than impulse invariance for your > application) or bilinear transform, or by nontraditional means, such as > FDLS.
Thanks I'll have a look at FDLS. Pete
On Wed, 29 Sep 2010 08:18:48 -0700, "Pete Fraser"  wrote:

>Is there any software around that designs Gaussian transition >filters? ScopeIIR and Matlab both deal with most of the >Zverev standards, but neither deals with GT.
What is the difference between a Gaussian filter and a Gaussian Transition filter? A Google search turns up only US Patent 4051458 for both "Gaussian Transition filter" and its citation, "'Filter Synthesis' by Ziev". Do you seek an analog implementation, or a digital implementation? An analog Bessel filter is an approximation to a Gaussian filter, and the approximation improves as the filter order increases. Since you asked for an IIR approximation, you could either approximate a Bessel filter by traditional means, such as step invariance (from context I suspect that step invariance will be better than impulse invariance for your application) or bilinear transform, or by nontraditional means, such as FDLS. Greg
Is there any software around that designs Gaussian transition
filters? ScopeIIR and Matlab both deal with most of the
Zverev standards, but neither deals with GT.

Any suggestions?

I'm looking to do 6dB and 12dB, up to 12th order,
and implementing as DF1 bi-quads.

Thanks

Pete