Re: Bilinear Transforms-> Möbius transforms
- To: mathgroup at smc.vnet.net
- Subject: [mg50807] Re: Bilinear Transforms-> Möbius transforms
- From: Roger Bagula <tftn at earthlink.net>
- Date: Wed, 22 Sep 2004 00:11:10 -0400 (EDT)
- References: <firstname.lastname@example.org>
- Reply-to: tftn at earthlink.net
- Sender: owner-wri-mathgroup at wolfram.com
It appear to be Fuchsian with determinant in lamda squared.
I usually similfy these by hand:
I think that's what you want.
These are called Möbius transforms and
are associated with the Poincare
Fuchsian groups are a big well studied area.
A tip is to multiply by (z/z) and (-1/Lamda)/(-1/Lamda)
to get a form where it is:
By bilinear they mean that the 2by2:
multiplies when the the functions are taken like f(g(z)).
These matrices are also associated as well with Klein groups and
Chris Williams wrote:
>I have an warped FIR filter with order around 1400 - however to unwarp
>this filter configuration for use on my data I need to apply the
>u' -> (z^-1 - lambda)/(1-lambda*z^-1)
>So essentially each unit delay becomes an all-pass element.
>I've substituted in the transform into a transfer function expression
>for my filter, and now I want to get the transfer function back into the
>normal form of a fraction of polynomials of z.
>I've tried Together and Simplify without much success. Has anyone
>accomplished something similar - any help would be greatly appreciated ;)
>Cheers and thanks,
Respectfully, Roger L. Bagula
tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/
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