Principle of the MLS method

The acoustic parameters of a linear system (such as a room) can be obtained through the impulse response h(t) between a source and a receiver. To obtain this response, an infinite number of different excitations have been used, such as the explosion of an air balloon, a gunshot, a firecracker… but the fidelity or repeatability of these methods may not be adequate.

The MLS (Maximum Length Sequence) method is based on the cross-correlation between an input excitation x(k) and an output signal y(k) through a linear system, where the excitation is a periodic pseudorandom signal represented in the form binary with 1 and -1. The cross correlation can be written as the following convolution:

Rxy(k) = Rxx(k) * h(k)

One of the main features of this method is the autocorrelation of the input signal, which is essentially a pulse (dirac delta). Therefore it can be considered that Rxx(k) ≈ δ(k). From this approximation it can be deduced that:

Rxy(k) ≈ δ(k) * h(k) = h(k)

Thus, if we calculate the cross-correlation between the MLS signal and the system output, we can obtain the impulse response of our linear system (such as our control room). Since x(k) is a known signal, using the fast Hadamard transform (FHT), we can quickly and efficiently calculate the impulse response of the system in question.