#55 Harmonize-Decompose Audio Signals with Global Amplitude and Frequency Modulations

A key building block in music transcription and indexing operations is the decomposition of music signals into notes. We model a note signal as a periodic signal with slow (frequency-selective) amplitude modulation and global frequency-warping. Global fre-quency-warping allows for an inharmonic frequency modulation, while the global amplitude modulation allows the various harmonics of the periodic signal to decay at different speeds. The global frequency-warping is achieved by a Laguerre transform (that has shown to fit stiffed strings inharmonic behavior). Assuming additive noise, the estimation of the model parameters and the optimization is performed in a Harmonize-Extract fashion. Simulations illustrate that the extraction technique oversteps the limitation of the global AM-FM representation and analysis techniques and allows the processing of inharmonic string instruments (e.g. piano).