[LAU] jack/oversampling

[Fons Adriaensen]

On Sun, Mar 16, 2014 at 07:50:57PM +0100, Jörn Nettingsmeier wrote:
 
> i don't understand this. can you elaborate? what is "blt"?

Bi-Linear Transform, a mathematical trick used to transform
the transfer function of an analog filter (in the s-domain)
into that of a digital one (in the z-domain). 

It introduces a 'warping' of the frequency axis. If A(f)
is the frequency response of the analog filter, and D(f)
that of the digital one, they will be different but there
is a function F(f) such that D(F(f)) = A(f). And it's 
always possible to arrange things such that the 'defining'
point of the FR (the -3 dB point, or the center frequency)
is correct - by applying the inverse of F(f).

For low frequencies F(f) = f, so the two filter are the
same. But as f->inf, F(f)->Fs/2. So filters in the upper
part of the frequency range will have a different shape
of the FR. For example a standard 2nd order parametric
will have a symmetric shape when plotted on a log frequency
scale, but the equivalent digital one won't if the center
frequency is high. But there is no reason to say that one
is 'better' than the other, there is no reason why any 
digital filter used in audio processing should be an exact
copy of an analog one.

Ciao,

-- 
FA

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It's also a pipe-dream, founded on self-delusion, nerd hubris
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