Re: Audio Low Frequency Instability

robert bristow-johnson wrote:
On Nov 13, 9:24 pm, Dirk Bruere at NeoPax <dirk.bru...@xxxxxxxxx>
wrote:
robert bristow-johnson wrote:
...
dunno if it will solve your particular low-frequency problem, but i
have found for audio (where the most interesting frequencies are often
7 or 8 octaves below Nyquist) is to use trig identities to express all
of the terms with (1 - cos(2*pi*f0/Fs)) in terms of something with
sin() instead. it requires a little change in the architecture of the
filter.

Thanks. That's a neat trick!

well, i didn't really spell it out but all's i was thinking of is the
same trick i did for accurately expressing frequency response at low
frequencies. i posted something about that a while ago:

http://groups.google.com/group/comp.dsp/browse_frm/thread/8c0fa8d396aeb444/a1bc5b63ac56b686

where the main idea is to replace

cos(w) <-- 1 - 2*(sin(w/2))^2

where w = 2*pi*f/Fs is the low frequency in the frequency response.
but now we replace w with w0=2*pi*f0/Fs where f0 is the very low
resonant frequency of the audio filter so we are replacing

cos(w0) <-- 1 - 2*(sin(w0/2))^2

in the filter coefficients and expressing all of the "1" terms with
direct paths in the signal flow graph. then, if you maintain some
kind of pseudo-floating-point with 2*(sin(w0/2))^2 (shifting bits
right after multiplying with scaled up versions of those tiny numbers)
you'll be able to implement an accurate filter even for low values of
w0.

that's the trick.

r b-j


Takes me back 35 yrs to my maths "A" level exams.
I'll have to dig out all my old trig books.
I can certainly see how people make a career out of DSP. It's one thing to understand such stuff, but another to think it up. Reminds me why I gave up physics.

--
Dirk

http://www.transcendence.me.uk/ - Transcendence UK
Remote Viewing classes in London
.

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