Approximation by a Sum of Complex Exponentials Utilizing the Pencil of Function Method

摘要

The approximation of a function by a sum of complex exponentials, in general, is a nonlinear optimization problem. The optimization problem, however, is linearized through the application of the pencil of function method. This noniterative method yields the best exponential approximation for a given order of approximation. The method differs radically from the classical Wiener least squares approach in the sense that exponents calculated by the pencil of function method are directly proportional to the integrated squared error in the approximation. As the integrated squared error approaches zero, the exponents calculated by the pencil of function method approach the best least squares exponents in a continuous fashion. Among the advantages of the method are its natural insensitivity to noise in the data and explicit determination of the signal order. Examples are presented to illustrate the stability of this technique especially when noise is present in the data.