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The Center for Studies in Music Technology at Yale Research Abstract
Igor Popovict, Ronald Coifman* and Jonathan Bergert t Center for Studies in Music Technology, Yale University * Department of Mathematics, Yale University
The applications we propose aim at providing a high-level symbolical interface to digital audio. Issues of representation and automated transcription are considered and discussed in relationship to the methods proposed.
Finally, we discuss feasibility of real-time facility for polyphonic pitch-tracking and score-following and implications in interactive performance situations.
In a previous paper we have reported on our experience with applying local trigonometric bases (LTT) of Coifman and Meyer [Coifman, Meyer, Quake and Wickerhauser, Proceedings of the International Conference on Wavelets and Applications, Toulouse, 93] to the problem of denoising old analog recordings [Berger, Coifman and Goldberg, ICMC 94 and Berger and Nichols, ICMC 94]. Here we present some results of applying similar techniques to pitch-tracking and timbre separation. Essentially, as in denoising we prepare the signal by performing an LTT on the discrete Fourier analysis of adequately overlapping, smoothly tapered segments of the signal. Having thus obtained a highly precise frequency localization, we then stop short of reconstructing the signal as performed in the denoising procedure. Instead, we generate weighted lists of active partials within each analysis window. Using basic pattern-matching procedures we then thread through these lists to obtain contiguous musical notes. We plan to extend this basic procedure to include timbre analysis and separation by matching on specific spectral combinations.
In our paper we compare different basis types (adapted local trigonometric and wavelet) regarding their respective capabilities to present a more or less clear image of the time-frequency information in musical signals and demonstrate the superiority of the approach described here over common simpler spectral analyses performed directly on the signal. With respect to real-time applications, we propose a hybrid technique of base switching, separating the task at hand into attack detection, using computationally inexpensive wavelet bases and subsequent frequency localization using LTT.
Coming soon: Examples of performance comparisons
Jonathan Berger
Comments to author: jberger@csmt.music.yale.edu
All contents copyright (C) 1995. Yale Center for Studies in Music Technology. All rights reserved. Revised: June 1, 1995