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An effect I've been working on
I am working with wavelet multiresolution analysis (WMRA) of musical timbre=
and I've been experiencing an interesting effect that someone might help me=
understand it better.
In a WMRA I decompose the original sound (e.g, a violin tone) into N wavele=
levels. Each wavelet level is roughly the original sound passed through the=
wavelet filter for that level.
The wavelet approach has several advantages over normal Fourier filtering=
since its filters have local support both in time and frequency, making it=
easy to locate transients on some frequency bands. Another important advant=
of wavelet filtering is its property of separating bands with quality
factor (Q) constant over the frequency axis, in a way the basilar membrane =
the inner ear also resolves frequency bands. This property makes wavelets
closer to ear's acoustic pre-processing, on stages before neural
Well, the effect comes up when I decide to listen the difference between th=
(1) the result of mixing the original tone with a reconstruction of the so=
from its wavelet coefficients (obtained in the forward transform) taking on=
the coefficients in level n and "clamping" other coefficients (from all oth=
levels) to zero value (this is reconstructing only the level n and mixing i=
to the original sound).
(2) the result of reconstructing the sound from all the coefficients in all=
levels except those in level n, which are zeroed (this is reconstructing th=
sound zeroing coefficients in level n).
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=
I am now trying to understand why eliminating information from one level so=
the same as summing the same information to the original sound!
Those who might have an oppinion towards the explanation of this effect, or=
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