Nonlinear time-frequency domain operators for decomposing sounds into loudness, pitch and timbre

We propose a method for decomposing instantaneous changes of sounds into three energy components, i.e., loudness, pitch, and timbre. These operators are derived from an eigenstructure analysis of the time-frequency gradient space (a 3-D space spanned by a modulus and partial derivatives of a wavelet transform). By several experiments, we found that they have superior resolution and sensitivity for segmenting speech into phonemes, characterizing dynamical nature of musical sounds, and so on