Analysis Of Stationary Processes Research Articles

A method of analysis of periodic processes in nonautonomous discrete-time systems with quantization

A method of analysis of stationary processes in systems with an arbitrary number of quantization levels in the presence of periodic external signals is proposed. The method is based on the representation of stationary oscillations in the form of an invariant set of nonlinear discrete point mappings. The spectral composition of the response of a system with an arbitrary period coupled with the discretization period through a rational relationship is calculated with the use of the discrete Fourier transform. The discrete Fourier transform is applied also to calculate nonlinear distortions. It is suggested to use the dependence of the ratio of the first-harmonic amplitude of the system’s steady-state response to the amplitude of the input-signal harmonic on the frequency of the input harmonic signal as the amplitude-frequency characteristic of a nonlinear system. In addition, it is suggested to use the dependence of the difference between the argument of the first harmonic of the system’s response and the initial phase of the input signal on the frequency of the input harmonic signal as the phase-frequency characteristic of the system. The usage of the method is illustrated by its application for the analysis of processes in first-and second-order circuits.

COHERENCE ANALYSIS OF STATIONARY PROCESSES WITH APPLICATIONS TO HYDROLOGY

Abstract Cross-spectral characteristics of the moving average and autoregressive processes are shown to be a powerful tool in testing and analyzing these types of generating processes in hydrology. Special significance has the coherence between two 1st order autoregressive processes which is shown to be equal to a constant independent of frequency.

Analysis of Stationary Processes with Mixed Spectra—Ii

SUMMARY We investigate the asymptotic power functions of three types of tests for detecting the presence of harmonic components superimposed on a nonuniform spectral density function. These power functions are tabulated for a range of values of the signal to noise ratio of the process, and each test is applied to several artificial series of the “mixed ”type with known structure.

The Analysis of Stationary Processes with Mixed Spectra—I

SUMMARY We consider a normal stationary process whose spectrum may contain harmonic components superimposed on a non-uniform continuous spectral density function. The problem of separating the discrete and continuous spectral components is discussed, and it is shown that the bandwidth of the spectral density function must be restricted, in relation to the number of observations, in order to make the problem tractable. Assuming only that this bandwidth is known, the presence of harmonic components is then detected by performing a “spectral” analysis on the tail of the autocovariance function, and a test is constructed based on the theory of random walks with absorbing barriers. A brief discussion of the case of non-normal processes is included.