A Note on “The Backus-Gilbert Inversion Method and the Processing of Sampled Data”

Xiang Gen Xia; Zhen Zhang

doi:10.1109/78.370633

A Note on “The Backus-Gilbert Inversion Method and the Processing of Sampled Data”

Xiang Gen Xia
, Zhen Zhang

University of Southern California

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this note, we show a sequence of interpolation formulas for the Backus-Gilbert (BG) method with 8-function kernels and penalty functions J(t, t’) = (t - t1)2k for integers k> 0. We show that the interpolation in the limit sense of k-ϖ is the Haar representation. The interpolation formulas are generalizations of the one obtained by Caccin et al. We also investigate the possibility of the BG method with 8-function kernels so that it is exactly the same as the Shannon sampling formula.

Original language	English
Pages (from-to)	776-778
Number of pages	3
Journal	IEEE Transactions on Signal Processing
Volume	43
Issue number	3
DOIs	https://doi.org/10.1109/78.370633
Publication status	Published - Mar 1995
Externally published	Yes

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Cite this

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A Note on “The Backus-Gilbert Inversion Method and the Processing of Sampled Data”

Abstract

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