On 8/20/2013 5:12 PM, radams2000@gmail.com wrote:

> In fact there is exactly such a filter, called "Transitional
> Butterworth-Thompson Filter", which has a factor that smoothly varies
> the step response between Butterworth and something close to
> Gaussian. Classic paper appeared in 1968. Used in many application,
> but not very well-known.

Another not so well known design is Legendre filter, which has the 
sharpest possible rolloff while keeping frequency response monotonic.
Interestingly, the problem of monotonic response has analytical solution.

Vladimir Vassilevsky
DSP and Mixed Signal Designs
www.abvolt.com

On 8/20/13 4:05 PM, FilterDan wrote:
> Apologies for being dangerous.

no need to.  being "dangerous" in this context is being effective.

a good book on analog filters combined with some means of mapping the 
analog filter to a digital filter can be an effective way to get 
something done.

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

combine that knowledge with the Bilinear Transform, and you'ld be pretty
dangerous, i think.

-- 

r b-j                  r...@audioimagination.com

"Imagination is more important than knowledge."



Thanks, I expected a response such as this, but I had no idea what it would
be. I know with absolute certainty that I am not some sort of inventive
genius, but topics like this are hard to research if you don't know the
right keyword. Now I've learned something, and so will anyone else reading
this post.

Apologies for being dangerous. 
Dan	 

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On Friday, August 16, 2013 12:38:54 PM UTC-4, FilterDan wrote:
> For those interested in filter design, I want to introduce you to the
> 
> Adjustable Gauss Polynomial. I am not selling anything here, and I would
> 
> imagine you could implement this in MatLab if you wanted to.
> 
> 
> 
> A couple of years ago I was experimenting with polynomial filters such as
> 
> the Butterworth. My goal was to find a polynomial that was more compatible
> 
> with digital filter design.
> 
> 
> 
> One thing I tried was to place equally spaced poles on the z plane in much
> 
> the same way as Butterworth poles are equally spaced on the s plane. It
> 
> worked fine, but not as good as the Adjustable Gauss.
> 
> 
> 
> The problem for me was that I wanted a filter with less distortion than the
> 
> Butterworth causes (less overshoot and ringing), but with less passband
> 
> roll off better selectivity than a Bessel. Of course, there is no middle
> 
> ground between the Bessel and Butterworth.  
> 
> 
> 
> The Adjustable Gauss solves this problem. It is capable of generating a
> 
> response anywhere from the Gauss to the Bessel to the Butterworth. You
> 
> simply set the parameter Gamma to give the desired response.
> 
> 
> 
> I can't paste in plots here, so this link will have to suffice. Frequency
> 
> responses and pole locations are given for various values of Gamma. The
> 
> algorithm is also given.
> 
> 
> 
> http://www.iowahills.com/7AdjustablePolyPage.html
> 
> 
> 
> Dan	 
> 
> 
> 
> _____________________________		
> 
> Posted through www.DSPRelated.com

In fact there is exactly such a filter, called "Transitional Butterworth-Thompson Filter", which has a factor that smoothly varies the step response between Butterworth and something close to Gaussian. Classic paper appeared in 1968. Used in many application, but not very well-known. 

Bob

On 8/16/13 9:38 AM, FilterDan wrote:
>
> The problem for me was that I wanted a filter with less distortion than the
> Butterworth causes (less overshoot and ringing), but with less passband
> roll off better selectivity than a Bessel. Of course, there is no middle
> ground between the Bessel and Butterworth.
>

"Of course"???  how are you so sure of that?  using the metaphor, it's 
like you didn't even step off the curb onto the middle ground that is there.

and "Gaussian filters" may very well lie in that middle ground.  i think 
there are other cases, but i don't have access to my Claude Lindquist 
book at the moment.  BTW, even though it's outa print (it *is* better 
than 3 decades old), you can get copies for cheap, it appears:

 
http://www.alibris.com/Active-Network-Design-with-Signal-Filtering-Applications-Claude-S-Lindquist/book/108704 


it's an excellent book for analog filters.  combine that knowledge with 
the Bilinear Transform, and you'ld be pretty dangerous, i think.

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

For those interested in filter design, I want to introduce you to the
Adjustable Gauss Polynomial. I am not selling anything here, and I would
imagine you could implement this in MatLab if you wanted to.

A couple of years ago I was experimenting with polynomial filters such as
the Butterworth. My goal was to find a polynomial that was more compatible
with digital filter design.

One thing I tried was to place equally spaced poles on the z plane in much
the same way as Butterworth poles are equally spaced on the s plane. It
worked fine, but not as good as the Adjustable Gauss.

The problem for me was that I wanted a filter with less distortion than the
Butterworth causes (less overshoot and ringing), but with less passband
roll off better selectivity than a Bessel. Of course, there is no middle
ground between the Bessel and Butterworth.  

The Adjustable Gauss solves this problem. It is capable of generating a
response anywhere from the Gauss to the Bessel to the Butterworth. You
simply set the parameter Gamma to give the desired response.

I can't paste in plots here, so this link will have to suffice. Frequency
responses and pole locations are given for various values of Gamma. The
algorithm is also given.

http://www.iowahills.com/7AdjustablePolyPage.html

Dan	 

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