Optimal reconstruction of signals from a set of linear measurements

Authors

  • A. V. Kovalenko Taras Shevchenko National University, Ukraine
  • V. N. Kurashov Taras Shevchenko National University, Ukraine

DOI:

https://doi.org/10.3103/S0735272704070118

Abstract

The problem of statistically optimal reconstruction of a signal based on its arbitrary linear projection is considered. The general solution to the problem is obtained in the form of the optimal reverse filter. The equation defining the filter represents an extension of the Wiener-Hopf equation to the case when N observations are a noise-bearing projection of a continuous random signal onto the space RN.

References

JERRI, A.J. "The Shannon sampling theorem — its various extensions and applications: a tutorial review," Proc. IEEE, v.65, n.11, p.1565-1596, 1977.

YU, S.-H.; HU, J.-S. "Optimal synthesis of a fractional delay FIR filter in a reproducing kernel Hilbert space," IEEE Signal Process. Lett., v.8, n.6, p.160-162, June 2001. DOI: https://doi.org/10.1109/97.923039.

KHURGIN, Y.I.; YAKOVLEV, V.P. Finite Functions in Physics and Engineering [in Russian]. Moscow: Nauka, 1971.

FRANKS, L.E. Signal Theory. Prentice Hall, 1969.

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Published

2004-07-11

Issue

Vol. 47 No. 7 (2004)

Section

Research Articles