Related papers: Quasi-Linear Transfer Function: A New Method for F…

Attosecond nonlinear Fourier transform (NFT) pump probe spectroscopy is an experimental technique which allows investigation of the electronic excitation, ionization, and unimolecular dissociation processes. The NFT spectroscopy utilizes…

Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms where a considerable amount of ancilla qubits and gates are often needed to form a Hilbert space large enough for high-precision results. Qubit recycling reduces…

The implementation of optimal statistical inference protocols for high-dimensional quantum systems is often computationally expensive. To avoid the difficulties associated with optimal techniques, here I propose an alternative approach to…

Linear, time-varying (LTV) systems composed of time shifts, frequency shifts, and complex amplitude scalings are operators that act on continuous finite-energy waveforms. This paper presents a novel, resource-efficient method for…

The rapid increase in the volume of data increased the size and complexity of the deep learning models. These models are now more resource-intensive and time-consuming for training than ever. This paper presents a quantum transfer learning…

In this study, we present a purely data-driven method that uses the Loewner framework (LF) along with nonlinear optimization techniques to infer quadratic with affine control dynamical systems that admit Volterra series (VS) representations…

Cut-and-project from a symmetric structure in a higher-dimensional space is a standard method for describing the structure of a large class of quasicrystals. By means of a novel localization procedure, we now show how local physical…

This article focuses on estimating relative transfer functions (RTFs) for beamforming applications. Traditional methods often assume that spectra are uncorrelated, an assumption that is often violated in practical scenarios due to factors…

Discrete Fractional Fourier Transforms (DFrFT) are universal mathematical tools in signal processing, communications and microwave sensing. Despite the excessive applications of DFrFT, implementation of corresponding fractional orders in…

The recently discovered phenomenon of nonlinear supratransmission consists in a sudden increase of the amplitude of a transmitted wave triggered by the excitation of nonlinear localized modes of the medium. We examine this process for the…

We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…

We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for…

The purpose of this paper is to investigate system identification for single-input-single-output general (active or passive) quantum linear systems. For a given input we address the following questions: (1) Which parameters can be…

In this paper, the regularization approach introduced recently for nonparametric estimation of linear systems is extended to the estimation of nonlinear systems modelled as Volterra series. The kernels of order higher than one, representing…

For the first time quaternions have been used for real-time frequency estimation, where the multi-dimensional nature of quaternions allows for the full characterization of three-phase power systems. This is achieved through the use of…

This paper attacks time-domain identification for interaction parameters of a heterogeneous networked dynamic system (NDS), with each of its subsystems being described by a continuous-time descriptor quadratic-bilinear time-invariant (QBTI)…

Long-term time series forecasting (LTSF) involves predicting a large number of future values of a time series based on the past values. This is an essential task in a wide range of domains including weather forecasting, stock market…

We investigate the spectral statistics of chaotic quasi one dimensional systems such as long wires. To do so we represent the spectral correlation function $R(\epsilon)$ through derivatives of a generating function and semiclassically…

The scattering transform is a non-linear signal representation method based on cascaded wavelet transform magnitudes. In this paper we introduce phase scattering, a novel approach where we use phase derivatives in a scattering procedure. We…

In the reinforcement learning literature, strong theoretical guarantees have been obtained for algorithms applicable to LTI systems. However, in the nonlinear case only weaker results have been obtained for algorithms that mostly rely on…