Recurrence Relations for Prolate Spheroidal Wave Functions
نویسندگان
چکیده
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...
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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.
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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 pape...
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The acquisition of functional magnetic resonance imaging (fMRI) data in a finite subset of k-space produces ring-artifacts and 'side lobes' that distort the image. In this article, we explore the consequences of this problem for functional imaging studies, which can be considerable, and propose a solution. The truncation of k-space is mathematically equivalent to convolving the underlying "true...
متن کاملA Generalization of the Prolate Spheroidal Wave Functions
Many systems of orthogonal polynomials and functions are bases of a variety of function spaces, such as the Hermite and Laguerre functions which are orthogonal bases of L2(−∞,∞) and L2(0,∞), and the Jacobi polynomials which are an orthogonal basis of a weighted L2(−1, 1). The associated Legendre functions, and more generally, the spheroidal wave functions are also an orthogonal basis of L2(−1, ...
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ژورنال
عنوان ژورنال: Journal of Mathematics and Physics
سال: 1953
ISSN: 0097-1421
DOI: 10.1002/sapm1953321269