17 Feb
2007
17 Feb
'07
2:23 a.m.
2007/2/17, Stefano D'Angelo <zanga.mail(a)gmail.com>om>:
2007/2/17, Camilo Polyméris
<cpolymeris(a)gmx.net>et>:
You are right. Compressors are the archetypical examples of
non-linear
filters. Delays, reverbs, chori, etc. are non-TI (they depend of past
input).
Still, there may be other properties which could be exploited for
optimization, as Stefano suggests. For example, you could collapse
several equalizers to one filter. Or if two consecutive plugins do FFT,
the first could pass the information to the second in the frequency domain.
Neither of these would work with current plugin architectures, though.
While I didn't think of plugins, but rather of more low-level components
(constructs of an audio-oriented programming language, or similar), I
have also been playing with a similar idea, but have not come to any
conclusions yet. I hope the linux-audio-dev comunity does.
Yes, compressors are non-linear because their output depends on the
value of the input, however reverbs, choruses, etc. are linear, no
matter that they depend on past input (also low-pass and high-pass
filters depend on past input really :-)
If you are not convinced a simple delay could have this transformation equation:
y(t) = sum ( alpha_k * delta (x - kT) )
with k >= 0. If you do
T(a*x1(t) + b*x2(t)) = a*y1(t) + b*y2(t) = a*T(x1(t)) + b*T(x2(t))
y1 and y2 are different only because of alpha_k coefficients, so the
filter is definitively linear :-)
Stefano
OOOOOps... what did I say....
I just woke up and I'm a bit confused.
the y(t) I was referring to is actually the h(t) of a delay :-)
Stefano
> Ok, i
get the context now. As you say, I'am both teacher and researcher,
> but my field is Software Engineering and my knowledge on theoretical DSP
> is not that mature, so don't take my DSP related statements so serious.
> To my level of knowledge, i could say that most of the plugins are not
> just LTI so, the kind of optimization you suggest would be not general
> just appliable to consecutive adjacent LTI systems. At the same time is
> something that may have a lot of sense in FreeADSP.
>
I actually don't know how many plugins are LTI, but, for example, a
lot of delays, reverbs, choruses, eq. filters, compressors, modulators
and "sound mixers" should be, and that's quite enough after all.
Consider that in the case of commonly used guitar effects the only
non-linear effects by their nature should be hardware-simulators
(valves, amps, etc.), distortions and synths.
Not sure at all, but i thought compressor was an example of non linear
transformation and they normally have an adaptive behavior which make them
not time invariant, so you cannot model it as a single H(f). It is very easy
to find a plugin which has been introduced non-linearity o time-variation
thought the main function (a filter, chorus, reverb...) is LTI. We are also
used other kinds of transformations such as sine shifting that are far from
linear also.