Time-frequency analysis of musical signals

Abstract

The major time and frequency analysis methods that have been applied to music processing are traced and application areas described. Techniques are examined in the context of Cohen's class, facilitating comparison and the design of new approaches. A trumpet example illustrates most techniques. The impact of different analysis methods on pitch and timbre examination is shown. Analyses spanning Fourier series and transform, pitch synchronous analysis, heterodyne filter, short-time Fourier transform (STFT), phase vocoder, constant-Q and wavelet transforms, the Wigner (1932) distribution, and the modal distribution are all covered. The limitations of windowing methods and their reliance on steady-state assumptions and infinite duration sinusoids to define frequency and amplitude are detailed. The Wigner distribution, in contrast, uses the analytic signal to define instantaneous frequency and power parameters. The modal distribution is shown to be a linear transformation of the Wigner distribution optimized for estimating those parameters for a musical signal model. Application areas consider analysis, resynthesis, transcription, and visualization. The more stringent requirements for time-frequency (TF) distributions in these applications are compared with the weaker requirements found in speech analysis and highlight the need for further theoretical research.