Pulse-transfer-function identification using discrete orthonormal sequences

A method for estimating the pulse-transfer function of a linear time-invariant sampled-data system from on-line input and output records is presented. The impulse response of the system is approximated by a finite linear combination of a set of discrete orthonormal sequences. These sequences can be generated by a chain of digital filters. The method is based on the fact that the system output at a given instant is the sum of the products of the system Fourier coefficients and the up-to-date input Fourier coefficients generated by passing the input through the chain of digital filters. The system model coefficients are chosen to give a least-squares fit between the actual system outputs and the model outputs. A recursive form of the estimation equations is derived. This allows the estimates to be updated easily with additional observations.