Informatica

The discrete Fourier transform (DFT) is used for determining the coefficients of a transfer function for n‐order singular linear systems, Ex⁽ⁿ⁾=Σi=1ⁿAix⁽ⁿ⁻¹⁾+Bu, where E may be singular. The algorithm is straight forward and easily can be implemented. Three step‐by‐step examples illustrating the application of the algorithm are presented.

The input–output relationship of the periodically time-varying (PTV) systems, impulse response of the PTV state–space system, and the transfer function of the PTV system are presented. A coefficient sensitivity is investigated by using a virtual PTV state-space system in which periodically time-varying coefficients are stochastically varied.

The present paper considers a constant-parameter estimation algorithm for an analog transfer function by discrete observations of the object's input and output variables. The algorithm is based on supplementary variables and least-squares methods. It is assumed, that the order of the transfer function is known and the derivatives of the input and output variables are non-measurable. The supplementary variables and their derivatives are constructed from discrete observations of the input and output variables by applying a numerically realized analog filter. Investigation results for the estimate properties are presented. The results were obtained by the method of statistical simulation.