Re: An effect I've been working on ("R.Rossi.A.Faria" )

Subject: Re: An effect I've been working on
From:    "R.Rossi.A.Faria"  <regis(at)LSI.USP.BR>
Date:    Thu, 20 Mar 1997 01:05:50 -0300

Ludger Solbach wrote:

> > The wavelet approach has several advantages over normal Fourier filtering
> > since its filters have local support both in time and frequency,
>
> Due to the uncertainty principle this ain't possible for linear
> time-frequency distributions.

Agreed, in theory: a signal can't be at the same time limited on both
domains.
But music itself is a "phenomenon" that involves limited-frequency
signals performing
over finite-time lengths. Or is this another theoretical discussion?

> > making it
> > easy to locate transients on some frequency bands.
>
> I would say, locating transients within single frequency bands is a thing
> one should not do at all, because it's the nature of transients that their
> spectrum is local in time and spread over the whole frequency axis.

So, how can I still listen/see (from graphics) with good localization in
the time
axis several "musical objects" better discriminated on some wavelet
levels and
smeared or very weak on others? (by musical objects I mean artifacts
caused by
mis-bowing a violin, touching another cord by mistake, and even special
kind of attacks, like staccatos, and accents, which are transients for
they long too short time).
Isn't that better say that some kind of transients can be located easier
on some
wavelet scales, even though they indeed exist over a wide frequency
range?

> > Curiously (or not, that's what I want to learn) the sounds (1) and (2) are
> > virtually the same, with differences under the threshold of perception for
> > some levels.
>
> You did not say if you are using orthogonal or non-orthogonal wavelets. I
> assume it's the latter, because in this case removing redundancy from the
> coefficients would not have a very strong effect on the audible content
> of the sound.

I am using orthogonal wavelets (Daubechies, Beylkin, Coiflets) on a
discrete approach
for the wavelet transform (not wavelet packets).

> In fact, this is even true for orthogonal wavelet expansions,
> if you drop the right (i.e. small) coefficients. This is basically how
> compression works.

This is true on my experiments specially for the (as you said) "small"
coefficients,
i.e. the least energetic, from the lower resolution levels (which are
also inaudible,
or close to this limen). Eliminate them does not make any important
effect on the sound.
But, the effect I said happens with higher resolution levels, fairly
audible ones.

I was not expecting such amount of discussions, and it is being good to
listen others
comment on this.
Best wishes 4 all,

Regis Rossi A. Faria
Computer Music Group - LSI
University of Sao Paulo
Brazil