Estimation of Frequencies in the Input and Output of Nonlinear Systems

The estimation of the frequencies from experimental data has attracted a great deal of attention for many years. As the output of a nonlinear system often contains not only the fundamental frequency of the input, but also its harmonics, it is therefore necessary to consider the estimation of the frequencies in both the input and the output. In this paper, the Cramer-Rao lower bound (CRLB) for the estimate of the frequencies using both the input and output data is derived and a procedure for estimating the frequencies in the input and output variables is presented. It is shown in the simulation example that the estimated frequencies of the input and output using the proposed method is close to the CRLB obtained using both input and output data, much smaller than that using just the output or input data.