- Title
- On the numerical computation of certain eigenfunctions of time and multiband limiting
- Creator
- Lakey, Joseph D.; Hogan, Jeffrey A.
- Relation
- Numerical Functional Analysis and Optimization Vol. 33, Issue 7-9, p. 1095-1111
- Publisher Link
- http://dx.doi.org/10.1080/01630563.2012.682133
- Publisher
- Taylor & Francis
- Resource Type
- journal article
- Date
- 2012
- Description
- A method is given for local numerical approximation of functions ψ that are multiband limited to a finite union of frequency bands and approximately time-limited to an interval [−T, T] in the sense that ψ is an eigenvalue of an operator that time limits then band limits to the corresponding sets, with an eigenvalue close to one. The local construction involves writing such an eigenfunction as an approximate sum of eigenfunctions of time- and band-limiting where the band-limiting interval has unit length. This is expressed as a discrete eigenvalue problem whose solution boils down to approximating local inner products of such functions and is reduced to the efficient numerical problem of approximating a corresponding local inner product of their sequences of integer samples. A numerical method for estimating the latter is also discussed.
- Subject
- bandlimited signals; multiband signals; Paley–Wiener space; prolate spheroidal wavefunctions; reproducing Kernal Hilbert space; sampling; time and multiband-limiting maximizers
- Identifier
- http://hdl.handle.net/1959.13/1326121
- Identifier
- uon:25363
- Identifier
- ISSN:0163-0563
- Language
- eng
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