equations for Butterworth IIR filters, where are they hiding?

I came across this webpage:
http://mymbs.mobeard.org/~pfisher/fov2-0010016c/fov2-0010016e/FOV2-001001A3/chapters/25katsianos/index.html
It lists the equations for the filter coefficients up to 5th order in
a form that seems relatively easy to implement.  I have come across other
derivations that seem more laborious.
Now unfortunately, the author has made the equations as GIFs with very
small size, and some of them are unreadable.
Has anybody come across these same formulae, where they are legible?
 

On Fri, 09 Sep 2016 21:34:04 -0700, mbjorn wrote:

> I came across this webpage:
> http://mymbs.mobeard.org/~pfisher/fov2-0010016c/fov2-0010016e/
FOV2-001001A3/chapters/25katsianos/index.html
> It lists the equations for the filter coefficients up to 5th order in a
> form that seems relatively easy to implement.  I have come across other
> derivations that seem more laborious.
> Now unfortunately, the author has made the equations as GIFs with very
> small size, and some of them are unreadable.
> Has anybody come across these same formulae, where they are legible?

If you're looking at coefficients and thinking "ooh! that's easy!" then 
that means that you're not planning on factoring out the transfer 
functions into 1st- and 2nd-order transfer functions and cascading them.

That means that you'll be disappointed when you implement the filters.

Go back to one of the "complicated" pages that shows you how to find the 
pole locations for a Butterworth, and use that to design a cascade of 2nd-
order sections.

-- 
Tim Wescott
Control systems, embedded software and circuit design
I'm looking for work!  See my website if you're interested
http://www.wescottdesign.com

On Friday, September 9, 2016 at 9:34:08 PM UTC-7, mbj...@y7mail.com wrote:
> I came across this webpage:
> http://mymbs.mobeard.org/~pfisher/fov2-0010016c/fov2-0010016e/FOV2-001001A3/chapters/25katsianos/index.html

(snip)

> Now unfortunately, the author has made the equations as GIFs with very
> small size, and some of them are unreadable.
> Has anybody come across these same formulae, where they are legible?

If I use zoom on the browser, control-+ or command-+, depending on your
computer, I can read them well enough. 

On 9/9/2016 11:34 PM, mbjorn@y7mail.com wrote:
> I came across this webpage:
> http://mymbs.mobeard.org/~pfisher/fov2-0010016c/fov2-0010016e/FOV2-001001A3/chapters/25katsianos/index.html
....
> Now unfortunately, the author has made the equations as GIFs with very
> small size, and some of them are unreadable.
> Has anybody come across these same formulae, where they are legible?
>

This is what happens when someone does not know how to use Latex,
and then use tex4ht to convert Latex to HTML and get pretty
math and web pages on the web.

https://www.ctan.org/pkg/tex4ht
https://en.wikipedia.org/wiki/TeX4ht

When people use word or Adobe GoLive 4 and other tools
not designed for Math, then the HTML result will be of lesser quality.

May be you can ask the author to write the page in Latex
and convert to HTML with tex4ht.

--Nasser

I know how find the poles of Butterworth. It was an assigment I had for an
abusive bully professor at a sandstone university back in 1976.
Anyway, I found the same equations in a Masters thesis. They apparently
were lifted from the textbook Stanley+2*Dougherty.
I only needed low-pass and high-pass for orders 1 to 5, so these are
exactly what I wanted. They actually work too.  I have come across a
few "cookbook" pages that were flawed, .e.g left out warping factor
or had equation upside-down.


On Saturday, September 10, 2016 at 10:57:46 PM UTC+8, Tim Wescott wrote:
> 
> If you're looking at coefficients and thinking "ooh! that's easy!" then 
> that means that you're not planning on factoring out the transfer 
> functions into 1st- and 2nd-order transfer functions and cascading them.
> 
> That means that you'll be disappointed when you implement the filters.
> 
> Go back to one of the "complicated" pages that shows you how to find the 
> pole locations for a Butterworth, and use that to design a cascade of 2nd-
> order sections.
> 

On Saturday, September 10, 2016 at 12:34:08 AM UTC-4, mbj...@y7mail.com wrote:
> I came across this webpage:
> http://mymbs.mobeard.org/~pfisher/fov2-0010016c/fov2-0010016e/FOV2-001001A3/chapters/25katsianos/index.html
> It lists the equations for the filter coefficients up to 5th order in
> a form that seems relatively easy to implement.  I have come across other
> derivations that seem more laborious.
> Now unfortunately, the author has made the equations as GIFs with very
> small size, and some of them are unreadable.
> Has anybody come across these same formulae, where they are legible?

Try this: http://www.claysturner.com/dsp/Butterworth%20Filter%20Formulae.pdf

mbjorn@y7mail.com writes:

> I came across this webpage:
> http://mymbs.mobeard.org/~pfisher/fov2-0010016c/fov2-0010016e/FOV2-001001A3/chapters/25katsianos/index.html
> It lists the equations for the filter coefficients up to 5th order in
> a form that seems relatively easy to implement.  I have come across other
> derivations that seem more laborious.
> Now unfortunately, the author has made the equations as GIFs with very
> small size, and some of them are unreadable.
> Has anybody come across these same formulae, where they are legible?

mbjorn,

I had these from another project and moved them into their own document.
Try this: 

  http://www.digitalsignallabs.com/butterworth.pdf

--Randy

-- 
Randy Yates, DSP/Embedded Firmware Developer
Digital Signal Labs
http://www.digitalsignallabs.com

Randy Yates <yates@digitalsignallabs.com> writes:

> mbjorn@y7mail.com writes:
>
>> I came across this webpage:
>> http://mymbs.mobeard.org/~pfisher/fov2-0010016c/fov2-0010016e/FOV2-001001A3/chapters/25katsianos/index.html
>> It lists the equations for the filter coefficients up to 5th order in
>> a form that seems relatively easy to implement.  I have come across other
>> derivations that seem more laborious.
>> Now unfortunately, the author has made the equations as GIFs with very
>> small size, and some of them are unreadable.
>> Has anybody come across these same formulae, where they are legible?
>
> mbjorn,
>
> I had these from another project and moved them into their own document.
> Try this: 
>
>   http://www.digitalsignallabs.com/butterworth.pdf
>
> --Randy

I just now looked at that page and this is probably not what you were
after. Oh well!
-- 
Randy Yates, DSP/Embedded Firmware Developer
Digital Signal Labs
http://www.digitalsignallabs.com