Related papers: Defining Fundamental Frequency for Almost Harmonic…
The generalizations of instantaneous frequency and instantaneous bandwidth to a bivariate signal are derived. These are uniquely defined whether the signal is represented as a pair of real-valued signals, or as one analytic and one…
We assume that the energy spectrum of a chaotic system undergoing symmetry breaking transitions can be represented as a superposition of independent level sequences, one increasing on the expense of the others. The relation between the…
We present the theory of how to achieve phase measurements with the minimum possible variance in ways that are readily implementable with current experimental techniques. Measurements whose statistics have high-frequency fringes, such as…
Fundamental frequency (f0) estimation from polyphonic music includes the tasks of multiple-f0, melody, vocal, and bass line estimation. Historically these problems have been approached separately, and only recently, using learning-based…
Black hole spectroscopy is the program to measure the complex gravitational-wave frequencies of merger remnants, and to quantify their agreement with the characteristic frequencies of black holes computed at linear order in black hole…
A subthreshold signal is transmitted through a channel and may be detected when some noise -- with known structure and proportional to some level -- is added to the data. There is an optimal noise level, called stochastic resonance, that…
The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
In the last years several estimation strategies have been formulated to determine the value of an unknown parameter in the most precise way, taking into account the presence of noise. These strategies typically rely on the use of quantum…
The fidelity amplitude is a quantity of paramount importance in echo type experiments. We use semiclassical theory to study the average fidelity amplitude for quantum chaotic systems under external perturbation. We explain analytically two…
The extension of the master stability function (MSF) to analyze stability of generalized synchronization for coupled nearly identical oscillators is discussed. The nearly identical nature of the coupled oscillators comes from some parameter…
We establish new sharp asymmetric Poincare inequalities in one-dimension with the computation of optimal constants and characterization of extremizers. Using the one-dimensional theory we develop a comprehensive study on fundamental…
Although one can formulate an intuitive notion of instantaneous frequency, generalizing "frequency" as we understand it in e.g. the Fourier transform, a rigorous mathematical definition is lacking. In this paper, we consider a class of…
A new concept, called quasi-linear transfer functions (QLTF), which can be used to characterize the output frequency behaviour of nonlinear systems, is introduced based on the well-known Volterra series representation. By using the new…
Reconstruction of undersampled periodic signals of unknown period is an important signal processing operation. It is especially difficult operation when the sequences of samples are short and no information on the inter-sequence time…
We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…
In the absence of a pure noise-free image it is hard to define what noise is, in any original noisy image, and as a consequence also where it is, and in what amount. In fact, the definition of noise depends largely on our own aim in the…
An alternative definition to the main frequency of an ultra-short laser pulse, named principal frequency ($\omega_P$), was recently introduced in E.G. Neyra, et al. Phys. Rev. A 103, 053124 (2021), resulting in a more transparent…
Objective. We identify two linked problems related to estimating the phase of the alpha rhythm when the signal after a specific event is unknown (real-time case), or corrupted (offline analysis). We propose methods to estimate the phase…
In this paper we suggest a new algorithm for determination of signal-to-noise ratio (SNR). SNR is a quantitative measure widely used in science and engineering. Generally, methods for determination of SNR are based on using of…