MLS principle

The acoustical parameters of a linear system (such as rooms), can be derived from the impulse response h(t) between an emitter and a receiver. To get this response, different kinds of excitations have been used such as a baloon explosion, gun shuts, bangers, ... but the accuracy and repeatavility of these methods may not be the best.

The MLS method (Maximum Length Sequence) is based on the cross correlation between an input signal x(k) and an output y(k) of a linear systema, where the excitation is a periodic pseudoaleatory signal, represented in a binary +1 i -1. The cross correlation can be shown as the following convolution:

R_xy(k) = R_xx(k) * h(k)

One of the best properties of this method is the autocorrelation of the binary signal, which is essentially an impulse(dirac delta). Hence, we can consider R_xx(k) ≈ δ(k). After this aproximation we can conclude that:

R_xy(k) ≈ δ(k) * h(k) = h(k)

Hence, if we calculate the cross correlation between the MLS signal and the system's output, we'll reach the impulse response. As x(k) is a known signal, using the fast Hadamard Transform (FHT), we can easily measure our system's impulse response.