Periodic signal extraction with global amplitude and phase modulation for music signal decomposition

A key building block in music transcription and indexing operations is the decomposition of the music signal into notes. We model a note signal as a periodic signal with (slow) global variation of amplitude (reflecting attack, sustain, decay) and frequency (limited time warping). The bandlimited variation of global amplitude and frequency is expressed through a subsampled representation and parameterization of the corresponding signals. Assuming additive white Gaussian noise, a maximum likelihood approach is proposed for the estimation of the model parameters and the optimization is performed in an iterative (cyclic) fashion that leads to a sequence of simple least-squares problems. Particular attention is paid to the estimation of the basic periodic signal, which can have a non-integer period, and the estimation of the amplitude signal with guaranteed positivity.