[music-dsp] Tweakable filters of higher orders?

[Joshua Scholar]

I'm no expert in this, but it's my impression that you can do much better
than cascading identical lower order filters.  Instead make an optimum high
order filter and then factor it into lower order filters...  I believe the
math is that this is always possible.

I've done this before (turned a high order filter into a cascade of lower
order ones) - I just looked up the math for it online and use Maxima to do
the calculations.
The result was a filter with identical response, but with less sensitivity
to round off error.

It's not entirely free.  The operations count of the lower order filter
cascade is higher than the single higher order filter it replaced.

----- Original Message ----- 
From: Nigel Redmon
To: a list for musical digital signal processing
Sent: Tuesday, September 28, 2004 11:28 PM
Subject: Re: [music-dsp] Tweakable filters of higher orders?


Yes, that is the usual thing to do--higher order filters get too
sensitive to coefficient precision. Most DSP texts point this out, and
suggest using series or parallel combinations of lower order filters. I
wanted to add that--it may or may not be obvious--when you cascade
several lower order filters, remember that the frequency cutoff moves
(because it's defined as the -3dB points, and since the cascade changes
the slope...).


On Sep 28, 2004, at 3:17 PM, Koen Tanghe wrote:

> On Sunday, September 26, 2004 1:46 AM [GMT+1=CET],
> Koen Tanghe <xxxkoen at smartelectronix.comxxx> wrote:
>
>> Can I just use a cascade
>> of multiple identical instances of a biquad to get "sharper" filters?
>> Or
>> are there any special things to do?
>
> Well, that's what I ended up with for now. Appears to work fine...
> Koen

--
dupswapdrop -- the music-dsp mailing list and website:
subscription info, FAQ, source code archive, list archive, book reviews, dsp
links
http://shoko.calarts.edu/musicdsp
http://ceait.calarts.edu/mailman/listinfo/music-dsp