Fast least squares FIR system identification

If finite impulse response (FIR) system identification is performed by minimizing the squared error between the measured system output, a set of least-squares normal euqations to be solved for the FIR system coefficients is obtained. If the assumed FIR system is of duration M samples, the usual solution for the M least squares simultaneous equations requires a number of computational operations proportional to M³and storage of normal equation coefficients proportional to M². The set of normal equations has an underlying structure, though, that can be exploited to yield a solution with computational operations proportional to M²and storage proportional to M. The outline of such an algorithm is presented here.