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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  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  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.