Primitive maximum-length sequences and pseudo-random signals

Abstract

Primitive maximum-length sequences in a Galois field GF(q) are defined as the simplest maximum-length sequences in the field, and their nature and properties are demonstrated. Primitive pseudo-random signals are then defined as signals generated from primitive maximum-length sequences by converting the field elements into signal levels. It is shown that the harmonic properties of a primitive pseudo-random signal define the harmonic properties of all pseudo-random signals generated from the same field with the same field element conversions. This leads to a procedure for designing pseudo-random signals with desirable properties for system identification that simply involves designing primitive pseudo-random signals with the same properties. The design procedure is described, and illustrated by primitive maximum-length sequences and pseudo-random signals in the field GF(7).