A new algorithm for the reconstruction of bandlimited functions and their Hilbert transform

Author

Boche, Holger ; Protzmann, Marcus

Author_Institution

Fakultat fur Inf. und Math., Friedrich-Schiller-Univ., Jena, Germany

Volume

46

Issue

2

fYear

1997

fDate

4/1/1997 12:00:00 AM

Firstpage

442

Lastpage

444

Abstract

This paper presents a new algorithm which permits the reconstruction of a hand-limited function from samples taken at not necessarily regularly spaced intervals, and also the recovery of the Hilbert transform of the function. For example, this enables the reconstruction of the real or the imaginary part of the dielectric permeability by means of the Kramers-Kronig relations. Regardless of the given sampling values, the algorithm converges in L₂ as well as pointwise and even. In contrast to known solutions, the algorithm requires no computation of Fourier integrals. Only a system of linear equations has to be solved in each iteration step. The approximating functions are distinguished by minimal energy. The new algorithm also applies to two-dimensional functions

Keywords

Hilbert transforms; Kramers-Kronig relations; electromagnetic fields; iterative methods; EM fields; Hilbert transform; Kramers-Kronig relations; approximating functions; bandlimited functions; dielectric permeability; iteration step; linear equations; sampling values; two-dimensional functions; Convergence; Dielectrics; Discrete transforms; Electrical engineering; Electromagnetic fields; Hilbert space; Image reconstruction; Integral equations; Permeability; Sampling methods;

fLanguage

English

Journal_Title

Instrumentation and Measurement, IEEE Transactions on

Publisher

ieee

ISSN

0018-9456

Type

jour

DOI

10.1109/19.571880

Filename

571880