A specialized fast cross-correlation for acoustical measurements using coded sequences

In acoustics applications, binary maximal-length sequences and related sequences are increasingly used for acoustics system identification tasks. A number of coded sequences, such as binary maximal-length related sequences and ternary sequences possess two-valued or pulselike autocorrelation functions. It is this correlation property that is exploited in most of acoustical applications. However, the length of some of these sequences is not directly suitable for FFT-based cross-correlation algorithms. This paper explores using standard FFTs to calculate the cross-correlation between two periodic finite-length sequences of equal length, where the lengths of the sequences are not a power of 2. We apply our specialized correlation algorithm to analyze data collected in a room-acoustic environment to simultaneously obtain impulse responses between multiple sources and multiple receivers.