Download Separating Piano Recordings into Note Events Using a Parametric Imitation Approach In this paper we present a working system for separating a piano recording into events representing individual piano notes. Each note is parameterized with a transient-plus-harmonics model that, should all the parameters be reliably estimated, would produce near perfect reconstruction for each note as well as for the whole recording. However, interference between overlapping notes makes it hard to estimate parameters from their combination. In this work we propose to assess the estimability of sinusoidal parameters via their apparent degree of interference, estimate the estimable ones using algorithms suitable for different interference situations, and infer the hard-to-estimate parameters from the estimated ones. The outcome is a sequence of separate, parameterized piano notes that perceptually highly resemble, if are not identical to, the notes in the original recording. This allows for later analysis and processing stages using algorithms designed for separate notes.
Download Piecewise Derivative Estimation of Time-Varying Sinusoids as Spline Exponential Functions This paper discusses the estimation of non-stationary sinusoidal parameters. We formulate a piecewise version of the distributive derivative algorithm, which is used to analyse non-stationary sinusoidal signals and estimate their frequencies and log amplitude derivatives over a long duration as spline functions, and apply this algorithm for the estimation of instantaneous frequencies, amplitudes and phase angles. Test results show that the piecewise derivative algorithm provides better estimation than the previous non-piecewise version at lower computation cost.