Sumraary--Properties and methods of generation of pseudo-random binary signals are discussed. A theory of linear modelling is developed for multivariable systems in which these signals form the inputs. Modelling with delay operators and exponential weighting function operators is considered. Experimental results are presented to illustrate the theory.
I. INTRODUCTION
A STRUCTURE which, when subjected to the same input signals as a system, produces signals identical to the output signals of the system is a perfect model of the system. In practice, it is impossible to obtain a model of a physical system which performs perfectly: the actual performance of a model depends on the sophistication of its structure and the nature of the input signals.
The simplest form of model structure is a linear one, which is satisfactory in many situations. For linear models, the superposition principle allows each pair of input and output signals to be considered separately, and the problem of modelling a multivariable system is therefore decomposed into a number of elemental problems, each of modelling a system with single input and output signals.
In order that a multivariable model may be unequivocally synthesized from the individual models obtained in this way, it is necessary that the crosscorrelation function of each pair of input signals is identically zero. For other demonstrable reasons, it is also desirable that each input signal has a single impulse autocorrelation function. These are attributes of "white" noise signals to which the correlation functions of certain deterministic signals approximate, and it is the use of these "pseudo-random" signals in linear modelling which is now discussed.
The properties and use of such signals have received a considerable amount of attention in the digital communications field [1]. Previously reported work related to the present investigation is confined to conventional crosscorrelation analysis of systems with single input and output signals [2,3].