Time-Frequency Analysis for Music Signals: A Mathematical Approach
Monika D�rfler · Journal of New Music Research · 2001
This paper establishes a link between certain problems that arise when digital audio signals are processed, and a branch of mathematical theory, called Gabor analysis. Going back to the work of D. Gabor in 1946, Gabor analysis is based on the idea of representing arbitrary signals of finite energy in terms of building blocks which have a well-defined “center of gravity” in a time-frequency sense. Indeed, various widely used spectral domain methods correspond to the use of particular Gabor frames. The interpretation of this situation from the point of view of Gabor analysis makes the calculation of the so called dual window computationally efficient and postprocessing by a weighting function unnecessary. Furthermore the idea of locally adaptive sets of building blocks will yield a generalisation of spectral domain methods especially helpful in the investigation of music signals.