R. Kłosiński

Periodically time-varying two-terminals at a steady state, description and identification

The periodically time-varying two-terminal network at a steady state may be described with a circular parametric operator. Within the domain of discrete time, such operator takes the form of a real element matrix. A circular parametric operator may be transformed into the frequency domain. In this version, the quantitative assessment of mixing and generating of harmonics of input and output signals is possible. This paper presents the derivation and effects of a genuine algorithm for identification of circular parametric operators. Some results of computer simulations are presented.

Reconstruction of Nonlinearly Deformed Periodic Signals Using Inverse Circular Parametric Operators

The original method of the non-linear distortions correction is presented. Aperiodic steady state of the linear periodical time-varying system may be described using a circular parametric operator. Within the domain of discrete time, such an operator takes the form of a constant real entries matrix. This way of system characterization is adopted to describe the steady state of the non-linear system. For reconstructing distorted signals some inverse circular parametric operators are determined using an original identification algorithm based on the set of input and output signals. The non-linear system operation depends on input signal shape and amplitude, thus each operator is determined for the different, so called, basic input signal. The described method is effective in some situations, but it requires further research to improve accuracy.

The steady-state impedance operator of a linear periodically time-varying one-port network and its determination

The steady-state impedance operator of a linear periodically time-varying one-port network and its determination The main subject of the paper is the description and determination of the impedance operator of a linear periodically timevarying (LPTV) one-port network in the steady-state. If the one-port network parameters and the supply vary periodically with the same period, the network reaches a periodic steady state. However, the sinusoidal supply may induce a non-sinusoidal voltage or current. It is impossible to describe such a phenomenon by means of one complex number. A periodically time-varying one-port network working in a steady-state regime can be described with a circular parametric operator. Within the domain of discrete time, such an operator takes the form of a matrix with real-valued entries. The circular parametric operator can be transformed into the frequency domain using a two-dimensional DFT. This description makes it possible to quantitatively assess LPTV system input and output harmonics aliasing. The paper also presents the derivation and the proof of convergence of an iteration scheme for the identification of circular parametric operators. The scheme may be used to determine the impedance of an LPTV one-port network. Some results of computer simulations are shown.

Reconstruction of spectrum of the nonlinearly distorted periodic signals sampled non-coherently

Factors characterizing the electrical energy quality (e.g. THD) are determined on the basis of voltage and current signals spectrum. The spectrum estimation errors come from the spectrum leakage caused by the non-coherent sampling and distortions appearing in the input circuits of the measuring system. This paper concerns the problem of accurate reconstruction of the nonlinearly distorted signal spectrum. The proposed method of the periodic input signal reconstruction (e.g. the CT primary current) is based on the modeling of the nonlinear system in a periodic steady state by a set of circular parametric operators (CPOs). This method requires coherent sampling of the measured signal that is inconvenient because of the electro-energetic system natural frequency changes. To avoid this limitation the reconstruction calculations are transferred to the spectral domain. The spectrum of the reconstructed signal is determined by means of the spectral version of the CPO (i.e. the SCPO) on the basis of the spectrum of the distorted signal. A modified discrete Fourier transform (MDFT) is used to determine the distorted signal spectrum. The MDFT is designed for the non-coherently sampled signal high accuracy spectrum analysis. The DFT modification idea consists in the adjustment of base function frequencies of the Fourier series to the analyzed signal harmonics frequencies. Some results of experiments are included.