On the Identification Problem

Abstract

The identification problem involves the determination of the identity of a black box from the observation of its responses to a set of input signals. In this paper attention is focused on the identification of zero-memory multipoles and two-poles of class <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n_1</tex> . The test signals are sine waves of different amplitudes and frequencies, and the measured quanity is the describing function of the device. In the case of two-poles of class <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n_1</tex> , it is found that the describing function is related to the characteristic function by an integral equation of second order which can be solved explicitly by the use of the Fourier-Hankel transformation.