Instrument de-synthesis using wavelets - Pelletier, Emile (University of Ottawa (Canada), 2005)
Our point of departure is the concept of 'additive synthesis', which is the traditional explanation for the individual of 'timbre' or 'colour' of the sound of the various musical instruments. When an instrument sounds a note, one hears the note as if by itself, but this is not what is physically happening. What is in fact occurring is a complex waveform featuring a collection of harmonic frequencies, referred to as the spectrum. A synthesizer attempts to imitate the sound of a particular instrument by replicating the amplitudes of its harmonics. We use the term 'de-synthesis' to refer to the inverse procedure, computerized instrument identification. We describe an experiment that we designed and executed with M ATLAB to explore the hypothesis that a computer will be able to recognize an instrument by its characteristic timbre. The idea of applying wavelets to analyze music comes naturally since music consists of sound waves, and wavelets are wave shaped functions. We propose a mathematical model that can take certain musical instrument's attack and decay features into account that utilizes Malvar wavelets: Super Malvar wavelets. Super wavelets are superpositions of ordinary wavelets in some linear combination that can be treated as a wavelet in itself. (Abstract shortened by UMI.)
Keywords: Mathematics.