Reciprocal maximum-length sequence pairs for acoustical dual source measurements

In this paper we propose and demonstrate a method to obtain simultaneous dual source-receiver impulse responses in acoustical systems using binary maximum-length sequences (MLS). A binary MLS and its reversed-order sequence form a reciprocal MLS pair. Their correlation property includes a two-valued "pulse-like" autocorrelation function and a relatively smaller-valued cross-correlation function. This unique property, along with other number-theory properties, makes the reciprocal MLS pair suitable for simultaneous dual source cross-correlation measurements. In the measurement of a dual source system, each of the reciprocal MLS pairs simultaneously excite one of two separate sources, one or several receiver signals cross-correlate in turn with each of the MLS pairs, resulting in impulse responses associated with two separate sources. The proposed method is particularly valuable for system identification tasks with multiple sound/vibration sources and receivers that have to be accomplished in a limited time period. A fast algorithm called a fast MLS transform is exploited for the cross-correlation. In this paper we propose a fast MLS transform pair for the reciprocal MLS pairs. Its efficiency lies in the requirement of one single permutation matrix for a pair of two fast MLS transforms. Its feasibility and usefulness in the acoustical measurements are demonstrated using experimental results.