Empirical AM-FM decomposition of auditory signals

Cochlea, known as `fourier analyzer' in auditory system of mammals, codes the mechanical wave to electrical signals tonotopically. Meanwhile, the auditory coder also works in temporal mode, where envelope (E, i.e. amplitude modulation (AM)) and temporal fine structure (TFS, i.e. frequency modulation (FM)) are both significant but not exactly defined. In several recent researches (e.g. [Smith, et. al, 2002]), hilbert transform (HT) was utilized to extract the E and TFS cues. Though HT is mathematically rigorous, it is lack of clear physical meaning on AM-FM. This research introduces the empirical mode decomposition (EMD) to auditory research field. EMD was designed for analysis of non-linear and non-stationary data including natural sound. It is observed that the outputs of a auditory filter (e.g. Gammachirp), which was born as narrow-band filters, are approximately intrinsic mode functions (IMF) that admit well-behaved hilbert transforms (implying having physical significance). However, non-narrow-band filter (NNBF) output can be decomposed into two obvious IMFs or more, implying that HT is not suited to NNBF. EMD with HT provides auditory researchers one more perspective on AM-FM decomposition of auditory signals.# This work is supported by National Natural Science Foundation of China (11104316) and Shanghai Natural Science Foundation (11ZR1446000).