抄録
This paper proposes a sequential procedure for estimating frequency responses of linear discrete-time systems, the output of which is contaminated with a stationary noise having an unknown mean value.
A mathematical model of the system is formulated by setting a situation that the noisy steady-state output to a composite sinusoidal input is observed. Applying the least-squares approach to the model, the values of real and imaginary parts of the frequency response of the system are estimated simultaneously at the frequencies corresponding to the components of the input signal. A sequential procedure is given for on-line implementation. In it the estimates are updated every M samples, where M is the number of the samples in one period of the input signal.
It is shown that the estimates are unbiased and consistent under the following two conditions even if the mean of the noise is unknown:
1) the frequencies of the input signal are integral multiples of the basic frequency 2π/N, where N is the number of the samples in the measurement time,
2) the measurement time is integral multiple of the period of the input signal.
An example of digital simulation is given also to show the usefulness of the proposed procedure.
