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Re: What is the difference equation of a Butterworth filter?

• To: mathgroup at smc.vnet.net
• Subject: [mg27480] Re: What is the difference equation of a Butterworth filter?
• From: "John Doty" <jpd at w-d.org>
• Date: Tue, 27 Feb 2001 00:37:34 -0500 (EST)
• References: <972ge7$4kr@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <972ge7$4kr at smc.vnet.net>, "Elias Kyriakides"
<elias_kyriakides at hotmail.com> wrote:

> Can anybody provide me with the difference equation of a Butterworth
> filter? e.g. something like y[n] = a1x[n] +a2x[n-1] etc
> 
> Thanks, Elias
> 
> 

No. The Butterworth filter has a frequency response that is a rational
function of finite order. Such a response can be realized by differential
equations, but not by difference equations.

The Buttterworth filter is a classic utilizing the capabilities of analog
electronic components. Attempting to approximate it digitally probably
isn't a particularly useful exercise: digital filters have different
capabilities and limitations.

-- 
| John Doty		"You can't confuse me, that's my job."
| Home: jpd at w-d.org
| Work: jpd at space.mit.edu