On identification of certain nonlinear systems (Corresp.)

In the fields of communication and control there sometimes arises the problem of determining the characteristics of a time-invariant system from discrete records of its input and output during a limited interval of time, where the output data are contaminated with random noise. When this system is linear, we can use the convolution sum to obtain a characterization of the output as a linear combination of past inputs. Hill and McMurtry [4] showed that if we choose a Legendre binary noise sequence as input to a linear system, then the least squares approximation to the characterizing coefficients is expressible in a computationally feasible form, even when a large number of coefficients is involved. In this correspondence we characterize a nonlinear system by a generalization of the convolution sum and show that if we choose Golomb´s maximal linear recurring binary-noise sequence [2] as input, then the least squares approximation to the characterizing coefficients is expressible in a computationally feasible form. Thus, the maximal linear recurring sequence occupies the same role in investigating certain nonlinear systems that the Legendre sequence occupies in investigating linear systems.