In this article we propose a method to improve the accuracy of sinusoid modeling by introducing parameter variation models into both the analyzer and the synthesizer. Using the least-square-error estimator as an example, we show how the sinusoidal parameters estimated under a stationary assumption relate to the real nonstationary process, and propose a way to reestimate the parameters using some parameter variation model. For the synthesizer, we interpolate the parameters using the same model, with the phase unwrapping process reformulated to adapt to the change. Results show that the method effectively cuts down the systematic error of a conventional system based on a least-square-error estimator and the McAulay-Quatieri synthesizer.

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This paper reviews the derivative method and explores its capacity for estimating time-varying sinusoids of complicated parameter variations. The method is reformulated on a generalized signal model. We show that under certain arrangements the estimation task becomes solving a linear system, whose coefficients can be computed from discrete samples using an integration-by-parts technique. Previous derivative and reassignment methods are shown to be special cases of this generic method. We include a discussion on the continuity criterion of window design for the derivative method. The effectiveness of the method and the window design criterion are confirmed by test results. We also show that, thanks to the generalization, off-model sinusoids can be approximated by the derivative method with a sufficiently flexible model setting.

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This paper provides a method for comparing phase angles of harmonic sound sources. In particular, we propose an algorithm for decomposing the difference between two sets of phases into a harmonic part, which represents the phase progress of harmonic components, and a residue part, which represents all causes of deviations from perfect harmonicity. This decomposition allows us to compare phase alignments regardless of an arbitrary time shift, and handle harmonic and noise/inharmonic parts of the phase angle separately to improve existing algorithms that handles harmonic sound sources using phase measurements. These benefits are demonstrated with a new phase-based pitch marking algorithm and an improved time-scale and pitch modification scheme using traditional harmonic sinusoidal modelling.

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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.

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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.

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