Sinusoids are widely used to represent the oscillatory modes of music and speech. The estimation of the sinusoidal parameters directly affects the quality of the representation. A parabolic interpolation of the peaks of the log-magnitude spectrum is commonly used to get a more accurate estimation of the frequencies and the amplitudes of the sinusoids at a relatively low computational cost. Recently, Werner and Germain [1] proposed an improved sinusoidal estimator that performs parabolic interpolation of the peaks of a power-scaled magnitude spectrum. For each analysis window type and size, a power-scaling factor$p$is pre-calculated via a computationally demanding heuristic. Consequently, the power-scaling estimation method is currently constrained to a few tabulated power-scaling factors for pre-selected window sizes, limiting its practical applications. In this article, we propose a method to obtain the power-scaling factor$p$for any window size from the tabulated values. Additionally, we investigate the impact of zero-padding on the estimation accuracy of the power-scaled sinusoidal parameter estimator.

Estimating mixtures of damped chirp sinusoids in noise is a problem that affects audio analysis, coding, and synthesis applications. Phase-based non-stationary parameter estimators assume that sinusoids can be resolved in the Fourier transform domain, whereas high-resolution methods estimate superimposed components with accuracy close to the theoretical limits, but only for sinusoids with constant frequencies. We present a new method for estimating the parameters of superimposed damped chirps that has an accuracy competitive with existing non-stationary estimators but also has a high-resolution like subspace techniques. After providing the analytical expression for a Gaussian-windowed damped chirp signal's Fourier transform, we propose an efficient variational EM algorithm for nonlinear Bayesian regression that jointly estimates the amplitudes, phases, frequencies, chirp rates, and decay rates of multiple non-stationary components that may be obfuscated under the same local maximum in the frequency spectrum. Quantitative results show that the new method not only has an estimation accuracy that is close to the Cramér-Rao bound, but also a high resolution that outperforms the state-of-the-art.

Variational inference of a Bayesian linear dynamical system is a powerful method for estimating latent variable sequences and learning sparse dynamic models in domains ranging from neuroscience to audio processing. The hardest part of the method is inferring the model's latent variable sequence. Here, we propose a solution using matrix inversion lemmas to derive what may be considered as the Bayesian counterparts to the Kalman filter and smoother, which are particular forms of the forward-backward algorithm that have known properties of numerical stability and efficiency that lead to cost growing linear with time. Opposed to existing methods, we do not augment the model dimensionality, use Cholesky decompositions or inaccurate numerical matrix inversions. We provide mathematical proof and empirical evidence that the new algorithm respects parameter expected values to more accurately infer latent state statistics. An application to Bayesian frequency estimation of a stochastic sum of sinusoids model is presented and compared with state-of-the-art estimators.

We present a Bayesian filter for state space models with Laplace-distributed observation noise that is robust to heavy-tailed and outlier-ridden univariate time-series data. We analytically derive a closed-form expression of the exact posterior for a Laplace likelihood conditioned on a Gaussian prior. Posterior statistics are propagated forward in time by a proxy Gaussian density. The forward Kullback-Leibler divergence from the posterior to the Gaussian is minimized by matching their moments. The proposed method supports both linear and non-linear systems, and has a fast recursive structure analogous to the Kalman filter that enables online inference. Results show that the new method outperforms existing approximate inference methods, especially in challenging scenarios where the system's parameters are uncertain.

Matching Pursuit (MP) is a greedy algorithm that iteratively builds a sparse signal representation. This work presents an analysis of MP in the context of audio denoising. By interpreting the algorithm as a simple shrinkage approach, we identify the factors critical to its success, and propose several approaches to improve its performance and robustness. We present experimental results on a wide range of audio signals, and show that the method is able to yield results thats are competitive with other audio denosing approaches. Notably, the proposed approach retains a small percentage of the transform signal coefficients in building a denoised representation, i.e., it produces very sparse denoised results.

This paper examines complex non-negative matrix factorization (CMF) as a tool for separating overlapping partials in mixtures of harmonic musical sources. Unlike non-negative matrix factorization (NMF), CMF allows for the development of source separation procedures founded on a mixture model rooted in the complex-spectrum domain (in which the superposition of overlapping sources is preserved). This paper introduces a physically motivated phase constraint based on the assumption that the source's pitch is sufficient in specifying the phase evolution of the harmonics over time, uniting sinusoidal modelling of acoustic sources with the CMF analysis of their spectral representations. The CMF-based separation procedure, armed with this novel phase constraint, is demonstrated to offer a superior performance to NMF when employed as a tool for separating overlapping partials in the acoustic test cases considered.

In this paper, we present a unified view of three non-stationary sinusoidal parameter estimation methods which are based on taking linear transforms of a signal and its derivatives. These methods, the Distribution Derivative Method (DDM), the Generalized Derivative Method (GDM), and the Generalized Reassignment Method (GRM), are shown to be subcases of a more general method which results in a system of linear equations from which we can solve for the parameter estimators. While the GDM and GRM are known to be theoretically equivalent, we show that they are also equivalent to the DDM in one special case. Matrix formulations are established for the GDM and GRM with a polynomial log-amplitude, polynomial phase sinusoidal signal model, and a bias in previous frequency slope estimators is explicitly demonstrated.

This paper introduces an analysis/synthesis scheme for the reproduction of sounds generated by sustained contact between rigid bodies. This scheme is rooted in a Source/Filter decomposition of the sound where the filter is described as a set of poles and the source is described as a set of impulses representing the energy transfer between the interacting objects. Compared to single impacts, sustained contact interactions like rolling and sliding make the estimation of the parameters of the Source/Filter model challenging because of two issues. First, the objects are almost continuously interacting. The second is that the source is generally unknown and has therefore to be modeled in a generic way. In an attempt to tackle those issues, the proposed analysis/synthesis scheme combines advanced analysis techniques for the estimation of the filter parameters and a flexible model of the source. It allows the modeling of a wide range of sounds. Examples are presented for objects of various shapes and sizes, rolling or sliding over plates of different materials. In order to demonstrate the versatility of the approach, the system is also considered for the modeling of sounds produced by percussive musical instruments.

Classical guitarists vary plucking position to achieve different timbres from nasal and metallic - closer to the bridge - to round and mellow -closer to the middle of the string. An interesting set of timbre descriptors commonly used by guitarists seem to refer to phonetic gestures: thin, nasal, round, open, etc. The magnitude spectrum of guitar tones being comb-filter shaped, we propose to see the local maxima of that comb filter structure as vocal formants. When guitarists talk about a guitar sound as being round, it would mean that it sounds like a round-shaped-mouth sound, such as the vowel /O/. Although the acoustic systems of the guitar and of the voice mechanism are structurally different, we highlight the fact that guitar tones and a particular set of vowels display similar formant regions. We also investigate the possibility of applying some distinctive features of speech sounds to guitar sounds.

This paper provides a review of gestural control of sound synthesis in the context of the design and evaluation of digital musical instruments. It discusses research in various areas related to this field and equally focuses on four main topics: analysis of music performers' gestures, gestural capture technologies, real-time sound synthesis methods, and strategies for mapping gesture variables to sound synthesis input parameters. Finally, this approach is illustrated by presenting an application of this research to the control of digital audio effects.

We propose in this paper a new point of view which unifies two well known filter families for approximating ideal fractional delay filters: Lagrange interpolator filters (LIF) and Thiran allpass filters. We achieve this unification by approximating the ideal Fourier transform of the fractional delay according to two different Pade approximations: series expansions and continued fraction expansions, and by proving that both approximations correspond exactly either to the LIF family or to the allpass delay filters family. This leads to an efficient modular implementation of LIFs.

We describe a new method for very high quality speech synthesis, and the procedure used for the automatic acquisition of the rules. Our method retains positive aspects of both diphone LPC synthesis and calculation of formant trajectories. For each sequence /VC#/ or /#CV/, we apply a very precise, pitch synchronous, LP analysis, we represent each spectrum in terms of the parameters for a parallel formant syntheziser, and we extract formant trajectories from these data. At the synthesis stage, for any /V1CcV2/ sequence, trajectories are calculated by rule using the stored trajectories of /V1Cc#/ and /#CcV2/. The signal is computed according to the calculated trajectories with a high quality parallel formant syntheziser. We have synthesized singing voices, but the same procedure can be applied to speech.