Related papers: Prolate Spheroidal Wave Functions Associated with …
In classic graph signal processing, given a real-valued graph signal, its graph Fourier transform is typically defined as the series of inner products between the signal and each eigenvector of the graph Laplacian. Unfortunately, this…
A new approach to the theory of anisotropic exciton based on Fock transformation, i.e., on a stereographic projection of the momentum to the unit 4-dimensional (4D) sphere, is developed. Hyperspherical functions are used as a basis of the…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
The quadratic phase Fourier transform has gained much popularity in recent years because of its applications in image and signal processing. However, the QPFT is inadequate for localizing the quadratic phase spectrum which is required in…
Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the…
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…
This article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. Also an efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet.…
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…
Transient signals are often composed of a series of modes that have multivalued time-dependent instantaneous frequency (IF), which brings challenges to the development of signal processing technology. Fortunately, the group delay (GD) of…
Optoacoustic imaging technologies require fast and accurate signal pre-processing algorithms to enable widespread deployment in clinical and home-care settings. However, they still rely on the Discrete Fourier Transform (DFT) as the default…
Interaction between metal surface waves and periodic geometry of subwavelength structures is at the core of the recent but crucial renewal of interest in plasmonics. One of the most intriguing points is the observation of abnormal strong…
A Fourier transform method is introduced for a class of hybrid time-frequency methods that solve the acoustic scattering problem in regimes where the solution exhibits both highly oscillatory behavior and slow decay in time. This extends…
The space-time focusing of a (continuous) succession of localized X-shaped pulses is obtained by suitably integrating over their speed, i.e., over their axicon angle, thus generalizing a previous (discrete) approach. First, new Superluminal…
We propose a conceptual frame to interpret the prolate differential operator, which appears in Communication Theory, as an entropy operator; indeed, we write its expectation values as a sum of terms, each subject to an entropy reading by an…
New solutions of relativistic wave equations are obtained in a unified manner from generating functions of spinorial variables. The choice of generating functions as Gaussians leads to representations in the form of generalized fractional…
In this paper, we present an assortment of both standard and advanced Fourier techniques that are useful in the analysis of astrophysical time series of very long duration -- where the observation time is much greater than the time…
Superoscillations have roots in various scientific disciplines, including optics, signal processing, radar theory, and quantum mechanics. This intriguing mathematical phenomenon permits specific functions to oscillate at a rate surpassing…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
The direct detection of continuous gravitational waves from pulsars is a much anticipated discovery in the emerging field of multi-messenger gravitational wave (GW) astronomy. Because putative pulsar signals are exceedingly weak large…
We quantify the strength of the waves and their impact on the energy cascade in rotating turbulence by studying the wave number and frequency energy spectrum, and the time correlation functions of individual Fourier modes in numerical…