REPRESENTATION AND ANALYSIS OF SIGNALS PART XV. MATCHED EXPONENTS FOR THE REPRESENTATION OF SIGNALS,
Abstract
Approximation by sums of exponentials is con sidered from various points of view, such as the time-domain approximation problem of network synthesis, in which an analytic time function is to be approximated, or situations in which dis crete measured values of some dynamic process are to be smoothed and fitted using an ex ponential model. Specifically, we consider determination of 2N possibly complex constants (A(j),s(j)), such that for given N and f(t) or (f(i)), one or the other of two integral ex pressions is minimum over both the (A(j)) and the (s(j)). Prony's method for approximate determin ation of the exponents is exhaustively reviewed in all its forms. It is found that the integral expressions are rather insensitive functions of the (s(j)), making direct minimization difficult. For the continuous case, a new scalar function of the (s(j)) is found, which vanishes if and only if one of the expressions is a relative minimum or maximum. The computational advantages afforded by this property allow construction of a practical iterative process leading to the true optimum exponents. The procedure is illustrated for the continuous case, and extensions to the discrete case are discussed. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 30, 1963
- Accession Number
- AD0411431
Entities
People
- Robert N. Mcdonough
Organizations
- Johns Hopkins University