Generalized Prolate Spheroidal Functions
نویسنده
چکیده
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, GPSFs are often replaced by crude approximations. The purpose of this paper is to review the elements of computing GPSFs and associated eigenvalues. This paper is accompanied by open-source code.
منابع مشابه
Generalized and Fractional Prolate Spheroidal Wave Functions
An important problem in communication engineering is the energy concentration problem, that is the problem of finding a signal bandlimited to [−σ, σ] with maximum energy concentration in the interval [−τ, τ ], 0 < τ, in the time domain, or equivalently, finding a signal that is time limited to the interval [−τ, τ ] with maximum energy concentration in [−σ, σ] in the frequency domain. This probl...
متن کاملChromatic Series and Prolate Spheroidal Wave Functions
The Ignjatovic theory of chromatic derivatives and series is extended to include other series. In particular series of prolate spheroidal wave functions are used to replace the orthogonal polynomial series in this theory. It is extended further to prolate spheroidal wavelet series that enables us to combine chromatic series with sampling series.
متن کاملGeneralized prolate spheroidal wave functions for offset linear canonical transform in Clifford analysis
Prolate spheroidal wave functions (PSWFs) possess many remarkable properties. They are orthogonal basis of both square integrable space of finite interval and the Paley-Wiener space of bandlimited functions on the real line. No other system of classical orthogonal functions is known to obey this unique property. This raises the question of whether they possess these properties in Clifford analy...
متن کاملProlate Spheroidal Wave Functions In q-Fourier Analysis
In this paper we introduce a new version of the Prolate spheroidal wave function using standard methods of q-calculus and we formulate some of its properties. As application we give a q-sampling theorem which extrapolates functions defined on qn and 0 < q < 1.
متن کاملApproximations and Fast Algorithms
The key element in the design of fast algorithms in numerical analysis and signal processing is the selection of an eÆcient approximation for the functions and operators involved. In this talk we will consider approximations using wavelet and multiwavelet bases as well as a new type of approximation for bandlimited functions using exponentials obtained via Generalized Gaussian quadratures. Anal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017