An effect I've been working on

```Dear listters,

I am working with wavelet multiresolution analysis (WMRA) of musical timbre=
s,=20
and I've been experiencing an interesting effect that someone might help me=
=20
understand it better.
In a WMRA I decompose the original sound (e.g, a violin tone) into N wavele=
t=20
levels. Each wavelet level is roughly the original sound passed through the=
=20
wavelet filter for that level.
The wavelet approach has several advantages over normal Fourier filtering=
=20
since its filters have local support both in time and frequency, making it=
=20
easy to locate transients on some frequency bands. Another important advant=
age=20
of wavelet filtering is its property of separating bands with quality
factor (Q) constant over the frequency axis, in a way the basilar membrane =
in=20
the inner ear also resolves frequency bands. This property makes wavelets
closer to ear's acoustic pre-processing, on stages before neural
processing.

Well, the effect comes up when I decide to listen the difference between th=
e=20
following sounds:

(1) the result of mixing the original tone with a reconstruction of the so=
und=20
from its wavelet coefficients (obtained in the forward transform) taking on=
ly=20
the coefficients in level n and "clamping" other coefficients (from all oth=
er=20
levels) to zero value (this is reconstructing only the level n and mixing i=
t=20
to the original sound).

(2) the result of reconstructing the sound from all the coefficients in all=
=20
levels except those in level n, which are zeroed (this is reconstructing th=
e=20
sound zeroing coefficients in level n).

Curiously (or not, that's what I want to learn) the sounds (1) and (2) are=
=20
virtually the same, with differences under the threshold of perception for=
=20
some levels.

I am now trying to understand why eliminating information from one level so=
unds=20
the same as summing the same information to the original sound!

Those who might have an oppinion towards the explanation of this effect, or=
=20
got interested in helping, please let me know.=20

Best wishes 4 all,

Regis Rossi A. Faria
Computer Music Group
Laboratorio de Sistemas Integra=E1veis (LSI)
University of Sao Paulo
Brazil
regis@lsi.usp.br=09http://www.lsi.usp.br/~regis/regis.html
```