A note on “The Backus-Gilbert inversion method and the processing of sampled data”

Author

Xia, Xiang-Gen ; Zhang, Zhen

Author_Institution

Dept. of Electr. Eng. Syst., Univ. of Southern California, Los Angeles, CA, USA

Volume

43

Issue

3

fYear

1995

fDate

3/1/1995 12:00:00 AM

Firstpage

776

Lastpage

778

Abstract

We show a sequence of interpolation formulas for the Backus-Gilbert (BG), published in 1967, method with δ-function kernels and penalty functions J(t, t´)=(t-t´)^2k for integers X>0. We show that the interpolation in the limit sense of X→∞ is the Haar representation The interpolation formulas are generalizations of the one obtained by Caccin et al.(see ibid., vol.40, no.11, p.2823, 1992). We investigate the possibility of the BG method with δ-function kernels so that it is exactly the same as the Shannon sampling formula. We also examined the possibility of the exact reconstruction by the BG method for bandlimited signals

Keywords

function approximation; interpolation; signal reconstruction; signal sampling; δ-function kernels; Backus-Gilbert inversion method; Haar representation; Shannon sampling formula; bandlimited signals; interpolation formulas; penalty functions; sampled data processing; signal reconstruction; Circuits; Convolution; Discrete cosine transforms; Interpolation; Kernel; Multidimensional signal processing; Signal design; Signal processing algorithms; Speech processing; Very large scale integration;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.370633

Filename

370633