J Austral Math Soc Ser B 34 pp35--42, 1992.

An extremal problem concerning fininte dimensional subspaces of C[a, b] pertinent in signal theory

P. H. Halpern, R.N. Mohapatra, P. J. O'Hara and R. S. Rodriguez

Abstract

Increase in dimensionality of the signal space for a fixed bandwidth leads to exponential growth in the number of different signals which must be encoded. In this paper we determine the best subspace of orthogonal functions which can be used to minimise the worst ratio of peak power to RMS power. A mathematical formulation of this problem has been made and it has been found that the Fourier basis satisfies the required constraints of optimality in terms of form factor (peak/RMS ratio).

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Authors

P. H. Halpern

Central Florida Technical Services, Inc., 118 Old Hickory Court, Longwood, Florida 32750.

R.N. Mohapatra

R. S. Rodriguez

Department of Mathematics, University of Central Florida, Orlando, Florida 32816.

P. J. O'Hara

Deceased.