## 1 Introduction
Having been originally introduced as a set of adhoc models describing so called hidden periodicity, over the last decades, CS signal analysis has matured into a selfsustaining branch of science, whose milestones and further trends are described, respectively, in [32; 33]. The recently published comprehensive monograph by [PERSON] [34] provides a contemporary, detailed explanation of the foundations and state of the art developments in CS analysis. Some introductory CS examples, yet in the analysis of mechanical systems, may be found in [35], where the vibration signals of rotating machines were analyzed with advanced spectral techniques [36]. As it follows from many sources, cyclostationarity seems to be firmly associated with the concept of a second order harmonizable random process [37]. The ensemble expectation taken on its lag product varies in time and, more importantly, can be expressed as a periodic or almost periodic function [34]. Equivalent frequency representation can be given via the expansion into Fourier series, whose coefficients are functions dependent on the lag parameter. However, from a nonprobabilistic point of view, which is illuminated in book [38] by [PERSON], even deterministic periodic waveforms can be treated as first order CS processes. The goal of this paper is establishing the foundation of a novel method that aims at performing accurate and detailed power analysis of the elements of electric circuits under periodic excitation. The proposed method is based on complex Fourier series decomposition rather than either sine-cosine decomposition or a phasor representation of the harmonics constituting the periodic currents and voltages. Despite its formal complexity, CS analysis seems to be an extremely effective approach, since it helps to reveal elementary power components, obeying the conservation law. Such components can be directly used to the noncontroversial derivation of all other quantities typically exploited for power description. This paper demonstrates how the standard collection of CS characteristics can be adapted to build an effective tool for describing the power in the elements of an electric circuit under the first order CS processes of voltages and currents. This collection includes the cyclic correlation function and spectral correlation function, which are widely exploited for coping with second order CS processes. The period of the processes is assumed to be known. In the case of unknown period, as often happens in practice, one can take on an appropriate period estimator prior to tuning the model parameters. Such a period estimator can be implemented via either synchronous averaging [39] with CS detection [40; 41] or more promising techniques based on sample coherency analysis [42; 43]. The rest of the paper is organized as follows. The second section presents the theoretical model of voltage-current two-dimensional cross correlation function (CCF), which appears to be a specific extension of instantaneous power. Next, the cross spectral correlation density is derived in an explicit closed form, which allows redefining the common quantities used in the power analysis directly from its components. The particular case of linear time invariant elements is also briefly explained in Section 2. In Section 3, the evaluation of the suggested characteristics is illustrated with numerical examples, where a resonant parallel circuit is excited by different periodic waveforms. The discussion in Section 4 considers the extension of the power conservation law that the components of the spectral correlation functions obey. The paper ends with conclusions.