System identification using pseudorandom signals and the discrete Fourier transform

Abstract

The theory of estimation of the frequency response of a system as the ratio of the discrete Fourier transforms of its sampled output and input, when the input is a pseudorandom signal, is developed. The principal sources of error are identified, their effects on the estimates are determined, and methods of error correction and reduction are described. Properties of the discrete Fourier transforms of pseudorandom sequences derived from binary and ternary m sequences are obtained, and the suitability of the corresponding pseudorandom signals for use as test signals in this application is established. The use of fast Fourier-transform techniques for the reduction of computation time is discussed, and the relative performance of these techniques and the crosscorrelation method for the estimation of both frequency and impulse responses of systems is evaluated.