Related papers: Quadratic phase wave packet transform
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT…
We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new,…
The quantum Fourier transform (QFT) is a key primitive for quantum computing that is typically used as a subroutine within a larger computation, for instance for phase estimation. As such, we may have little control over the state that is…
In this paper we review recent developments in the statistical theory of weakly nonlinear dispersive waves, the subject known as Wave Turbulence (WT). We revise WT theory using a generalisation of the random phase approximation (RPA). This…
Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical…
The Hilbert transform has been one of the foundational transforms in signal processing, finding it's way into multiple disciplines from cryptography to biomedical sciences. However, there does not exist any quantum analogue for the Hilbert…
This report investigates the main definitions and fundamental properties of the fractional two-sided quaternionic Dunkl transform in two dimensions. We present key results concerning its structure and emphasize its connections to classical…
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…
A consistent constructive covariant description of neutrino flavour transition amplitude in vacuum is presented. To this end a special generalized relativistic wave packet is constructed with correct extension onto the higher spins. This…
Nonlinearity parameter tomography leads to the problem of identifying a coefficient in a nonlinear wave equation (such as the Westervelt equation) modeling ultrasound propagation. In this paper we transfer this into frequency domain, where…
Wavelet transforms are widely used in various fields of science and engineering as a mathematical tool with features that reveal information ignored by the Fourier transform. Unlike the Fourier transform, which is unique, a wavelet…
We discuss the advantages of using the approximate quantum Fourier transform (AQFT) in algorithms which involve periodicity estimations. We analyse quantum networks performing AQFT in the presence of decoherence and show that extensive…
Quaternionic signal processing provides powerful tools for efficiently managing color signals by preserving the intrinsic correlations among signal dimensions through quaternion algebra. In this paper, we address the quaternionic phase…
In recent years there has been a growing interest in the fractional Fourier transform driven by its large number of applications. The literature in this field follows two main routes. On the one hand, the areas where the ordinary Fourier…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
We propose three core ideas: 1. the wave-particle duality of the qudit quantum space; 2. the classification of all elementary quantum gates by ordered pairs of qudit functionals; 3. a new type of quantum gates called the "quantum wave…
In non-stationary signal processing, prior work has incorporated the quadratic-phase Fourier transform (QPFT) into the ambiguity function (AF) and Wigner distribution (WD) to enhance their performance. This paper introduces an advanced…
One of the key challenges in the area of signal processing on graphs is to design transforms and dictionaries methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier…
Different kinds of wave packet transforms are widely used for extracting multi-scale structures in signal processing tasks. This paper introduces the quantum circuit implementation of a broad class of wave packets, including Gabor atoms and…
This paper introduces a novel time-frequency distribution, referred to as the Two-Dimensional Non-Separable Quadratic Phase Wigner Distribution (2D-NSQPWD), formulated within the framework of the Two-Dimensional Non-Separable Quadratic…