Design of multilevel pseudorandom signals for specified harmonic content

Pseudorandom signals are used in system identification usually in their binary form, usually for the identification of linear systems and usually because of their correlation properties. Pseudorandom binary signals are unsuitable for the identification of nonlinear systems but pseudorandom ternary signals have been used for the purpose, exploiting their higher-order correlation properties. In contrast, system identification exploiting the harmonic properties of pseudorandom signals has received considerably less attention. The principal factor which militates against exploiting the harmonic properties of multilevel pseudorandom signals for system identification is the sheer complexity of the underlying theory and its dependence on the algebra of finite fields. To some extent, the difficulties can be circumvented by constructing sum and product tables to define the algebraic operations involved. These tables can be constructed for any Galois field with q field elements, where q is a power of a prime. The construction of such tables and their properties are discussed