Related papers: Compositional nonlinear audio signal processing wi…
Solving systems of non-autonomous ordinary differential equations (ODE) is a crucial and often challenging problem. Recently a new approach was introduced based on a generalization of the Volterra composition. In this work, we explain the…
Modulations are a critical part of sound design and music production, enabling the creation of complex and evolving audio. Modern synthesizers provide envelopes, low frequency oscillators (LFOs), and more parameter automation tools that…
A sound synthesis model for woodwind instruments is developed using modal decomposition of the input impedance, accounting for viscothermal losses as well as localized nonlinear losses at the end of the resonator. To extend the definition…
We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…
In this letter we address the numeric inversion of optoacoustic signals to initial stress profiles. Therefore we put under scrutiny the optoacoustic kernel reconstruction problem in the paraxial approximation of the underlying…
An effective modeling method for nonlinear distributed parameter systems (DPSs) is critical for both physical system analysis and industrial engineering. In this Rapid Communication, we propose a novel DPS modeling approach, in which a…
We investigate the probabilistic and analytic properties of Volterra processes constructed as pathwise integrals of deterministic kernels with respect to the H\"older continuous trajectories of Hilbert-valued Gaussian processes. To this…
This article introduces an effective generalization of the polar flavor of the Fourier Theorem based on a new method of analysis. Under the premises of the new theory an ample class of functions become viable as bases, with the further…
The range of potential applications of acoustic analysis is wide. Classification of sounds, in particular, is a typical machine learning task that received a lot of attention in recent years. The most common approaches to sound…
The nonlinear oscillator model allows a basic understanding of all nonlinear processes and can be adopted to analyse optical vibrational modes and electronic transition in molecules and crystals, in order to derive general properties of…
Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null…
In a number of data-driven applications such as detection of arrhythmia, interferometry or audio compression, observations are acquired indistinctly in the time or frequency domains: temporal observations allow us to study the spectral…
This paper discusses the use of absolutely one-homogeneous regularization functionals in a variational, scale space, and inverse scale space setting to define a nonlinear spectral decomposition of input data. We present several theoretical…
This paper develops a principle of similarity for the design of a nonlinear absorber, the nonlinear tuned vibration absorber (NLTVA), attached to a nonlinear primary system. Specifically, for effective vibration mitigation, we show that the…
This article introduces a nonparametric approach to multivariate time-varying power spectrum analysis. The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral…
Nonlinear physics plays an essential role in hearing, from sound signal generation to sound sensing to the processing of complex sound environments. We demonstrate that the evolution of the biological hearing sensors demonstrates a dramatic…
Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning…
The paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with introduction of new concepts like the smoothing operator and semi-harmonic…
Consider a time series of measurements of the state of an evolving system, x(t), where x has two or more components. This paper shows how to perform nonlinear blind source separation; i.e., how to determine if these signals are equal to…
We present the applications of methods from nonlinear local harmonic analysis for calculations in nonlinear collective dynamics described by different forms of Vlasov-Maxwell-Poisson equations. Our approach is based on methods provided the…