Computation of weighted moments of discrete-time systems using experimental data

For an unknown linear discrete-time system, a simple algorithm for computing the weighted moments of the system from experimental input-output data is derived. When the measured output is contaminated with noise and/or if a system has a long tail of impulse response, it is difficult to exactly obtain the time moments of output signals. To overcome this drawback, we suggest first introducing a digital filter to the measured output and then obtaining the weighted moments for both input and filtered output data. Subsequently the weighted moments of the discrete-time system are algebraically computed using both the input and output weighted moments. The proposed algorithm is applied to the identification of the parameters of a discrete-time low-order model from a rectangular pulse response with a random noise.