Measurement of Frequency Response Function Using Characteristic M-Sequences

Abstract

A simple method is proposed for determining the frequency response function G(jω) of a system using a pair of characteristic M-sequences.
When a characteristic M-sequence is sampled with q₁ and q₂, both of which are coprime with N, where N is the period of the M-sequence, the obtained pair of sequences have conjugate complex frequency spectrum. Making use of this fact, two characteristic M-sequences having conjugate complex frequency spectrum are applied to a system to be identified, and the output spectrums are calculated.
Taking the average of the products of the output spectrums, we can obtain the frequency response function of the system. Experimental results show a good agreement with the theoretical considerations.