Forums

variable gain in an Butterworth IIR

Started by Unknown September 10, 2006
Hi,
I'm not sure this has been hashed out before on comp.dsp, I searched
the archives but no luck.
so I'll ask:


I'm designing a butterworth filter using the typical analog prototype,
then converting it to LP/HP/BP/BS, then doing the bilinear transform
then separating out the zeros/poles into biquad sections.

So far so good (if I want maximum attenuation in my stop bands), but
what if I just want -20dB or -40 dB attentuation in my stop band ...
I'm unclear from the papers and texts that I'm using as references how
to achieve this ...

any ideas, papers, examples would be great!!!

thanks!!


polar.ninja@gmail.com wrote:


> > I'm designing a butterworth filter using the typical analog prototype, > then converting it to LP/HP/BP/BS, then doing the bilinear transform > then separating out the zeros/poles into biquad sections. > > So far so good (if I want maximum attenuation in my stop bands), but > what if I just want -20dB or -40 dB attentuation in my stop band ...
What you are trying to build is called the shoulder filter. You may think of it as of cascaded LPF and HPF, and derive the response accordingly. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
polar.ninja@gmail.com wrote:
> Hi, > I'm not sure this has been hashed out before on comp.dsp, I searched > the archives but no luck. > so I'll ask: > > > I'm designing a butterworth filter using the typical analog prototype, > then converting it to LP/HP/BP/BS, then doing the bilinear transform > then separating out the zeros/poles into biquad sections. > > So far so good (if I want maximum attenuation in my stop bands), but > what if I just want -20dB or -40 dB attentuation in my stop band ... > I'm unclear from the papers and texts that I'm using as references how > to achieve this ...
Ignore for the moment that a digital approximation of an analog filter is only an approximation. When you specify Butterworth, you specify a frequency response. The response you specify is not Butterworth, so one of your specifications has to give. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Jerry Avins <jya@ieee.org> wrote in news:CpidnfgmFaK-
BJnYnZ2dnUVZ_oCdnZ2d@rcn.net:

> polar.ninja@gmail.com wrote: >> Hi, >> I'm not sure this has been hashed out before on comp.dsp, I searched >> the archives but no luck. >> so I'll ask: >> >> >> I'm designing a butterworth filter using the typical analog prototype, >> then converting it to LP/HP/BP/BS, then doing the bilinear transform >> then separating out the zeros/poles into biquad sections. >> >> So far so good (if I want maximum attenuation in my stop bands), but >> what if I just want -20dB or -40 dB attentuation in my stop band ... >> I'm unclear from the papers and texts that I'm using as references how >> to achieve this ... > > Ignore for the moment that a digital approximation of an analog filter > is only an approximation. When you specify Butterworth, you specify a > frequency response. The response you specify is not Butterworth, so one > of your specifications has to give. > > Jerry
The only way you can change attenuation in the stop band and maintain the filter definition would be to change the order of the filter. -- Scott Reverse name to reply
"Scott Seidman" <namdiesttocs@mindspring.com> schrieb im Newsbeitrag 
news:Xns983B52376442Ascottseidmanmindspri@130.133.1.4...
> Jerry Avins <jya@ieee.org> wrote in news:CpidnfgmFaK- > BJnYnZ2dnUVZ_oCdnZ2d@rcn.net: > >> polar.ninja@gmail.com wrote: >>> Hi, >>> I'm not sure this has been hashed out before on comp.dsp, I searched >>> the archives but no luck. >>> so I'll ask: >>> >>> >>> I'm designing a butterworth filter using the typical analog prototype, >>> then converting it to LP/HP/BP/BS, then doing the bilinear transform >>> then separating out the zeros/poles into biquad sections. >>> >>> So far so good (if I want maximum attenuation in my stop bands), but >>> what if I just want -20dB or -40 dB attentuation in my stop band ... >>> I'm unclear from the papers and texts that I'm using as references how >>> to achieve this ... >> >> Ignore for the moment that a digital approximation of an analog filter >> is only an approximation. When you specify Butterworth, you specify a >> frequency response. The response you specify is not Butterworth, so one >> of your specifications has to give. >> >> Jerry > > > The only way you can change attenuation in the stop band and maintain the > filter definition would be to change the order of the filter. > > > -- > Scott > Reverse name to reply
You can just move the zeros toward the origin of the unit circle (z-plane) and you'll get less attenuation. Gerold
Gerold Schrutz wrote:
> "Scott Seidman" <namdiesttocs@mindspring.com> schrieb im Newsbeitrag > news:Xns983B52376442Ascottseidmanmindspri@130.133.1.4... >> Jerry Avins <jya@ieee.org> wrote in news:CpidnfgmFaK- >> BJnYnZ2dnUVZ_oCdnZ2d@rcn.net: >> >>> polar.ninja@gmail.com wrote: >>>> Hi, >>>> I'm not sure this has been hashed out before on comp.dsp, I searched >>>> the archives but no luck. >>>> so I'll ask: >>>> >>>> >>>> I'm designing a butterworth filter using the typical analog prototype, >>>> then converting it to LP/HP/BP/BS, then doing the bilinear transform >>>> then separating out the zeros/poles into biquad sections. >>>> >>>> So far so good (if I want maximum attenuation in my stop bands), but >>>> what if I just want -20dB or -40 dB attentuation in my stop band ... >>>> I'm unclear from the papers and texts that I'm using as references how >>>> to achieve this ... >>> Ignore for the moment that a digital approximation of an analog filter >>> is only an approximation. When you specify Butterworth, you specify a >>> frequency response. The response you specify is not Butterworth, so one >>> of your specifications has to give. >>> >>> Jerry >> >> The only way you can change attenuation in the stop band and maintain the >> filter definition would be to change the order of the filter. >> >> >> -- >> Scott >> Reverse name to reply > > You can just move the zeros toward the origin of the unit circle (z-plane) > and you'll get less attenuation.
Then it's not Butterworth any more. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
polar.ninja@gmail.com skrev:
> Hi, > I'm not sure this has been hashed out before on comp.dsp, I searched > the archives but no luck.
You are asking the wrong question. You are looking for a standard design technique that has been discussed here on numerous occation, see e.g. http://groups.google.no/group/comp.dsp/msg/dbaf979ba841b588 The problem you outline has nothing to do with "variable gain", it has to do with designing filters that comply to a specification. If you are serious about learning how to design filters, you will find the book that is mentioned in that post useful. Rune
"Jerry Avins" <jya@ieee.org> schrieb im Newsbeitrag 
news:i8idndMvt85ICJjYnZ2dnUVZ_sGdnZ2d@rcn.net...
> Gerold Schrutz wrote: >> "Scott Seidman" <namdiesttocs@mindspring.com> schrieb im Newsbeitrag >> news:Xns983B52376442Ascottseidmanmindspri@130.133.1.4... >>> Jerry Avins <jya@ieee.org> wrote in news:CpidnfgmFaK- >>> BJnYnZ2dnUVZ_oCdnZ2d@rcn.net: >>> >>>> polar.ninja@gmail.com wrote: >>>>> Hi, >>>>> I'm not sure this has been hashed out before on comp.dsp, I searched >>>>> the archives but no luck. >>>>> so I'll ask: >>>>> >>>>> >>>>> I'm designing a butterworth filter using the typical analog prototype, >>>>> then converting it to LP/HP/BP/BS, then doing the bilinear transform >>>>> then separating out the zeros/poles into biquad sections. >>>>> >>>>> So far so good (if I want maximum attenuation in my stop bands), but >>>>> what if I just want -20dB or -40 dB attentuation in my stop band ... >>>>> I'm unclear from the papers and texts that I'm using as references how >>>>> to achieve this ... >>>> Ignore for the moment that a digital approximation of an analog filter >>>> is only an approximation. When you specify Butterworth, you specify a >>>> frequency response. The response you specify is not Butterworth, so one >>>> of your specifications has to give. >>>> >>>> Jerry >>> >>> The only way you can change attenuation in the stop band and maintain >>> the >>> filter definition would be to change the order of the filter. >>> >>> >>> -- >>> Scott >>> Reverse name to reply >> >> You can just move the zeros toward the origin of the unit circle >> (z-plane) and you'll get less attenuation. > > Then it's not Butterworth any more. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
a digital implementation of a butterworth filter isn't butterworth anyway! Gerold
Gerold Schrutz wrote:
> "Jerry Avins" <jya@ieee.org> schrieb im Newsbeitrag > news:i8idndMvt85ICJjYnZ2dnUVZ_sGdnZ2d@rcn.net... >> Gerold Schrutz wrote:
...
>> Then it's not Butterworth any more.
...
> a digital implementation of a butterworth filter isn't butterworth anyway!
Did you read in my first message in this thread "Ignore for the moment that a digital approximation of an analog filter is only an approximation"? Had I not already written that, I would have written "Then it's not a digital approximation of Butterworth any more." Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;