Exploiting number-theoretical properties of binary M sequences for acoustical measurements

Abstract

Due to their excellent number-theoretical properties, binary maximum-length sequences (M sequences) have received wide acceptance in many scientific and engineering fields. Since the introduction of M-sequence measuring technology into acoustics community in 1979 [J. Acoust. Soc. Am. 66, 497–500 (1979)] by one of the authors (MRS), advanced measurement techniques have emerged in fields such as architectural acoustics, physical acoustics, ocean acoustics, and ultrasonics. As excitation, binary M sequences carry much more signal power within a single period than signals used in the pulse-echo method. Together with its inherent cross-correlation mechanism, this technique enables high noise immunity. A fast algorithm, called a fast M-sequence transform, can be applied for performing the cross correlation. A number of noteworthy properties of binary M sequences such as shift-and-add, Zech’s logarithm, decimation, reciprocity, permutation, auto and cross correlation will be described with the emphasis of their applications in various acoustical measurement.