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Filter diagonalization with finite Fourier transform eigenfunctions
Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Quantum Chemistry.
2006 (English)In: Journal of Mathematical Chemistry, ISSN 0259-9791, E-ISSN 1572-8897, Vol. 40, no 1, 43-47 p.Article in journal (Refereed) Published
Abstract [en]

Below, we briefly report on the progress in the development of the Filter Diagonalization technique when filtering is carried out with the aid of Finite Fourier Transform (FFT) eigenfunctions. During recent years interest in these functions, also known as 'prolates', or 'slepians', has increased among scientists doing research in the field of signal processing. The main explanation to this follows from the set of very special extremal and orthogonality properties exibited by the FFT eigenfunctions. Recent results of Walter and Shen on sampling with prolate spheroidal functions will necessary produce a new wave of interest. In the presented, Filter diagonalization machinery, we show that the sampling formula of Walter and Shen simplifies essentially the computation of matrix elements as certain 2D-integrals involving FFT eigenfunctions.

Place, publisher, year, edition, pages
2006. Vol. 40, no 1, 43-47 p.
Keyword [en]
filter diagonalization, spectral analysis, auto-correlation function, finite Fourier transform, prolates, sampling theorem
National Category
Chemical Sciences
URN: urn:nbn:se:uu:diva-155800DOI: 10.1007/s10910-006-9124-7ISI: 000239432000005OAI: oai:DiVA.org:uu-155800DiVA: diva2:428292
Available from: 2011-06-30 Created: 2011-06-30 Last updated: 2011-06-30Bibliographically approved

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