An effect I've been working on (Regis Rossi Alves Faria )

Subject: An effect I've been working on
From:    Regis Rossi Alves Faria  <regis(at)LSI.USP.BR>
Date:    Tue, 18 Mar 1997 13:41:39 -0300

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(at)

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