Related papers: Discrete Prolate Spheroidal Wave Functions: Furthe…
Prolate spheroidal wave functions (PSWFs) play an important role in various areas, from physics (e.g. wave phenomena, fluid dynamics) to engineering (e.g. signal processing, filter design). One of the principal reasons for the importance of…
Since the early 1960s, the fields of signal processing, data transmission, channel equalisation, filter design and others have been technologically developed and modernised as a result of the research carried out by D. Slepian and his…
In this work, we first give various explicit and local estimates of the eigenfunctions of a perturbed Jacobi differential operator. These eigenfunctions generalize the famous classical prolate spheroidal wave functions (PSWFs), founded in…
Prolate spheroidal wave functions (PSWFs) play an important role in various areas, from physics (e.g. wave phenomena, fluid dynamics) to engineering (e.g. signal processing, filter design). Even though the significance of PSWFs was realized…
The discrete prolate spheroidal sequences (DPSSs) are a set of orthonormal sequences in $\ell_2(\mathbb{Z})$ which are strictly bandlimited to a frequency band $[-W,W]$ and maximally concentrated in a time interval $\{0,\ldots,N-1\}$. The…
In this work, we first give some mathematical preliminaries concerning the generalized prolate spheroidal wave function (GPSWFs). These set of special functions have been introduced in [16] and [7] and they are defined as the infinite and…
For fixed $c,$ Prolate Spheroidal Wave Functions (PSWFs), denoted by $\psi_{n, c},$ form an orthogonal basis with remarkable properties for the space of band-limited functions with bandwith $c$. They have been largely studied and used after…
For fixed $c,$ the Prolate Spheroidal Wave Functions (PSWFs) $\psi_{n, c}$ form a basis with remarkable properties for the space of band-limited functions with bandwidth $c$. They have been largely studied and used after the seminal work of…
For a fixed reals $c>0$, $a>0$ and $\alpha>-\frac{1}{2}$, the circular prolate spheroidal wave functions (CPSWFs) or 2d-Slepian functions as some authors call it, are the eigenfunctions of the finite Hankel transform operator, denoted by…
For fixed $c,$ the Prolate Spheroidal Wave Functions (PSWFs) $\psi_{n, c}$ form a basis with remarkable properties for the space of band-limited functions with bandwidth $c$. They have been largely studied and used after the seminal work of…
As demonstrated by Slepian et. al. in a sequence of classical papers, prolate spheroidal wave functions (PSWFs) provide a natural and efficient tool for computing with bandlimited functions defined on an interval. Recently, PSWFs have been…
As demonstrated by Slepian et. al. in a sequence of classical papers, prolate spheroidal wave functions (PSWFs) provide a natural and efficient tool for computing with bandlimited functions defined on an interval. As a result, PSWFs are…
In this paper, we introduce the prolate spheroidal wave functions (PSWFs) of real order $\alpha>-1$ on the unit ball in arbitrary dimension, termed as ball PSWFs. They are eigenfunctions of both a weighted concentration integral operator,…
The main result of this thesis is an efficient protocol to determine the frequencies of a signal $C(t)= \sum_k |a_k|^2 e^{i \omega_k t}$, which is given for a finite time, to a high degree of precision. Specifically, we develop a theorem…
The prolate spheroidal wave functions, which are a special case of the spheroidal wave functions, possess a very surprising and unique property [6]. They are an orthogonal basis of both $L^2(-1,1)$ and the Paley-Wiener space of bandlimited…
In the present paper, we introduce the multidimensional Clifford prolate spheroidal wave functions (CPSWFs) defined on the unit ball as eigenfunctions of a Clifford differential operator and provide a Galerkin method for their computation…
In this work, we first give some mathematical preliminairies concerning the generelized prolate spheroidal wave functions(GPSWFs). This set of special functions have been introduced in [21]and [13] and they are defined as the infinite and…
We prove a weak version of Hardy's uncertainty principle using properties of the prolate spheroidal wave functions (PSWFs). We describe the eigenvalues of the sum of a time limiting operator and a band limiting operator acting on L2(R). A…
An algorithm for computing eigenvalues and eigenfunctions of the angular spheroidal wave equation, based on a known but scarcely used method, is developed. By requiring the regularity of the wave function, represented by its series…
Generalized Prolate Spheroidal Functions (GPSF) are the eigenfunctions of the truncated Fourier transform, restricted to D-dimensional balls in the spatial domain and frequency domain. Despite their useful properties in many applications,…