Related papers: The hyperanalytic signal
Elucidating a connection with nonlinear Fourier analysis, we extend a well known algorithm in quantum signal processing to represent measurable signals by square summable sequences. Each coefficient of the sequence is Lipschitz continuous…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
A method is proposed to characterize a high-dimensional quantum channel with the aid of classical light. It uses a single nonseparable input optical field that contains correlations between spatial modes and wavelength to determine the…
We use the matching method to investigate the first-order phase transition in holographic superconductor and superfluid. We first use the simple holographic superconductor model to describe the matching method and mention how to see the…
Unitary Fourier transform lies at the core of the multitudinous computational and metrological algorithms. Here we show experimentally how the unitary Fourier transform-based phase estimation protocol, used namely in quantum metrology, can…
In this paper, we present a signal processing framework for directed graphs. Unlike undirected graphs, a graph shift operator such as the adjacency matrix associated with a directed graph usually does not admit an orthogonal eigenbasis.…
Classical Graph Signal Processing (GSP) provides a robust framework for analyzing signals on irregular domains, utilizing the graph Fourier transform as a cornerstone for spectral analysis and filtering. However, as data structures grow in…
The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the…
In this study, we experimentally investigate the application of a transient signal with complex frequencies to the absorption and transmission of sound waves. Indeed, the emission of a wave with an exponentially varying amplitude in time is…
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and…
Bicoherence analysis is a well established method for identifying the quadratic nonlinearity of stationary processes. However, it is often applied without checking the basic assumptions of stationarity and convergence. The classic…
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
Coherent control of wave transmission and reflection is crucial for applications in communication, imaging, and sensing. However, many practical scenarios involve partially coherent waves rather than fully coherent ones. We present a…
Several notions of "analytic" functor introduced recently in the literature fit into the graphic fourier transform context presented in [D].
In the digital world, signals are discrete and finite. The Fourier representation of discrete and finite signals is FT convolution of the finite sampling function and the continuous signal. Conventionally, finite sampling is treated as a…
Excitation of waves in a three-layer acoustic wavegide is studied. The wave field is presented as a sum of integrals. The summation is held over all waveguide modes. The integration is performed over the temporal frequency axis. The…
In this paper, we define a new transform called the Gabor quaternionic Fourier transform (GQFT), which generalizes the classical windowed Fourier transform to quaternion valued-signals, we give several important properties such as the…
In this paper, we propose the Fourier frequency vector (FFV), inherently, associated with multidimensional Fourier transform. With the help of FFV, we are able to provide physical meaning of so called negative frequencies in…
The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed…