TIME-FREQUENCY ANALYSIS OF MUSICAL SIGNALS

The major time and frequency analysis methods that have been applied t o music processing are traced and application areas described Techniqu es are examined in the context of Cohen's class, facilitating comparis on and the design of new approaches. A trumpet example illustrates mos t techniques. The impact of different analysis methods on pitch and ti mbre examination is shown. Analyses spanning Fourier series and transf orm, pitch synchronous analysis, heterodyne filter, short-time Fourier transform (STFT), phase vocoder, constant-Q and wavelet transforms, t he Wigner distribution, and the modal distribution are all covered. Th e limitations of windowing methods and their reliance on steady-state assumptions and infinite duration sinusoids io define frequency and am plitude are detailed. The Wigner distribution, in contrast, uses the a nalytic 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 mu sical signal model. Application areas consider analysis, resynthesis, transcription, and visualization. The more stringent requirements for time-frequency (TF) distributions in these applications are compared w ith the weaker requirements found in speech analysis and highlight the need for further theoretical research.