This paper proposes a cyclostationary based approach to power analysis carried out for electric circuits under arbitrary periodic excitation. Instantaneous power is considered to be a particular case of the two-dimensional cross correlation function (CCF) of the voltage across, and current through, an element in the electric circuit. The cyclostationary notation is used for deriving the frequency domain counterpart of CCF—voltage–current cross spectrum correlation function (CSCF). Not only does the latter exhibit the complete representation of voltage–current interaction in the element, but it can be systematically exploited for evaluating all commonly used power measures, including instantaneous power, in the form of Fourier series expansion. Simulation examples, which are given for the parallel resonant circuit excited by the periodic currents expressed as a finite sum of sinusoids and periodic train of pulses with distorted edges, numerically illustrate the components of voltage–current CSCF and the characteristics derived from it. In addition, the generalization of Tellegen’s theorem, suggested in the paper, leads to the immediate formulation of the power conservation law for each CSCF component separately.
The methods for generating estimator for radio source location based on digital processing of signals received at various points in space are one of the main areas of multi-position radar systems’ research. Nowadays the above-mentioned methods that can provide the highest accuracy among the others are subject of interest. So, the mean square error usually serves as a measure of accuracy, which allows formulating a convenient, for mathematical transformations, quality criteria and synthesizing the algorithms. The traditional estimation algorithms have a multi-stage character, and they are based on the formation of optimal estimators for time and phase delays of the signals and their subsequent conversion to the source coordinates. The research has the modern approaches of the development of new positioning algorithms to guarantee the achievement of the minimum mean square error and do not create excessive computing load.
This article addresses the problem of estimating the spectral correlation function (SCF), which provides quantitative characterization in the frequency domain of wide-sense cyclostationary properties of random processes which are considered to be the theoretical models of observed time series or discrete-time signals. The theoretical framework behind the SCF estimation is briefly reviewed so that an important difference between the width of the resolution cell in bifrequency plane and the step between the centers of neighboring cells is highlighted. The outline of the proposed double-number fast Fourier transform algorithm (2N-FFT) is described in the paper as a sequence of steps directly leading to a digital signal processing technique. The 2N-FFT algorithm is derived from the time-smoothing approach to cyclic periodogram estimation where the spectral interpolation based on doubling the FFT base is employed. This guarantees that no cyclic frequency is left out of the coverage grid so that at least one resolution element intersects it. A numerical simulation involving two processes, a harmonic amplitude modulated by stationary noise and a binary-pulse amplitude-modulated train, demonstrated that their cyclic frequencies are estimated with a high accuracy, reaching the size of step between resolution cells. In addition, the SCF components estimated by the proposed algorithm are shown to be similar to the curves provided by the theoretical models of the observed processes. The comparison between the proposed algorithm and the well-known FFT accumulation method in terms of computational complexity and required memory size reveals the cases where the 2N-FFT algorithm offers a reasonable trade-off.
The paper is aimed at building analytical models of signals possessing complex types of digital modulation within the framework of the cyclostationary approach. The proposed analytical approach includes procedures leading to closed-form analytical expressions of spectral correlation functions (SCF), which are functions depending on two arguments: frequency and cyclic frequency. They describe the probabilistic properties of the analyzed signals assuming the signals can be modeled as realizations of second-order cyclostationary random processes (CSRP). The proposed approach of obtaining both normal and conjugate SCFs is based on the modified shaping operator technique, which turns out to be an effective tool applied to CSRP analysis. The technique handles the constructing the variety of the typically used in practice CSRPs in the form of chained transforms applied to one or several independent CSRPs of known characteristics by means of relatively simple operations, widely expressed in signal and systems theory. These operations performed over signals, which are assumed to be realizations of the CSRP, correspond to the transformations of their SCF, whose formulae are presented in the paper. The paper also reveals the exact analytical expressions obtained for the normal and conjugate SCF of OFDM signals with cyclic prefix (CP) whose subcarriers are modulated using BPSK and QPSK methods. By example of OFDM signal with a CP and QPSK subcarrier modulation, a quantitative comparison was carried out between the analytical SCF assembled according to the model formula and its estimate obtained by a numerical simulation using the estimation method based on the mixed two-dimensional fast Fourier transform. It is shown that the SCF estimate converges in root-mean sense to the constructed analytical model with an increase in the duration of the analyzed signal data sample.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.