Wavelet transforms for bioacoustic signal processing

Abstract

Wavelet transforms (WT) are natural tools for analysis of bioacoustic signals. In analysis of transient signals and nonstationary stochastic processes it is important to know not only what are the frequency content transients but when did these transient signals occur. The importance of representation of signals on the time-frequency plane, not only on frequency or time axes, is now widely accepted. Linear time-frequency analysis of transient signals (signals with time-varying frequency content) can be based on short-time Fourier transforms (STFT) and generalized Gabor transforms (GT). Wavelet transform analysis is analogous to STFT and GT analysis, except WTs represent signals on time and scale plane. In time-frequency analysis there is a tradeoff between time and frequency resolution. WTs have the advantage that they have constant time-frequency resolution over a wide frequency range. WT represent constant fractional or constant Q frequency analysis, thus efficiently analyzing a wideband of frequencies. Continuous wavelet transforms are linear transforms that can be inverted. In this tutorial paper basic properties of continuous and discrete wavelet transforms are reviewed, basic issues between Fourier transform techniques are discussed and disadvantages and advantages of WT are pointed out. [Work supported by ONR, Code 333.]