We apply methods for determining concealed periodicities in zero crossings to spectral analysis of signals. The proposed methods increase confidence in the estimates obtained by using preliminary computation of "quasispectra" and nonlinear signal processing.In certain areas of science and technology, e.g., geophysics, optics, and audio-and video-signal processing, it is necessary to determine the parameters of quasiperiodic signals, i.e., signals that are additive mixtures of several sinusoidal waves that have time-varying parameters with white noise. The conventional approach to solution of this problem uses methods of detecting hidden periodicities, which has advantages over FFT methods in that there is no need to establish a period for the signal; the period can be determined during processing. Among the disadvantages of the method of detecting hidden periodicities is that it requires cumbersome computation and a large sample to achieve a given resolution [1].At the present time, considerable attention has been drawn to a method of detecting hidden periodicities by computing the number of zero crossings in a measurement signal, since the method of detecting hidden periodicities from zero crossings has an excellent resolution capability, has a lower computational cost (since it only requires addition operations), and inherits the properties of the ordinary method of detecting hidden periodicities. This makes it necessary to determine whether the method can be used for spectral analysis of signals.The fundamentals of the method of detecting hidden periodicities from zero crossings were presented by Rice in [2], where the statistical and probabilistic characteristics of signals taken to be mixtures of sinusoidal waves mixed with normally distributed white noise were determined. In particular, Rice derived a formula for determining the mathematical expectation of the number of zero crossings for such signals. Study of the problem was continued by White, Raynel, Bendat, and others. Bendat [3], for example, generalized Rice's results to the case of sinusoids with variable parameters and obtained a simpler formula for the mathematical expectation for the number of zeros, as well as a formula for the mathematical expectation of the mean square number of zero crossings by a process under investigation.The zeros problem was subsequently further studied by B. Kedem, who extended previous results to discrete time and concluded that the number of times a signal crosses zero provides an idea of the spectral properties of the signal, which makes it possible to use zeros of a signal to estimate its spectrum. In particular, it was shown in [4] that the mathematical expectation for the number of zeros D of a signal composed of white noise is connected to the spectral function of the signal by the following relation:where E(*) is the mathematical expectation operator, F(co) is the spectral function of the signal, N is the size of the sample, co is the relative angular frequency, i.e., the frequency normalized by the quantization...

A method is proposed for evaluating the frequency of periodic trends based on the number of zero crossings by a signal. This method is distinguished by low computation time requirements. Test results demonstrate the possible use of this method in practical applications.Initial data processing is needed in measurement-data systems to reduce the volume of data transmitted along communication lines. An important aspect of this processing is the detection of trends with their subsequent elimination. Identifying a constant component and trends of a simple linear form is not diffi cult and procedures for detecting these are well known and widely used [1]. A more diffi cult problem, at least computationally, is the identifi cation of periodic trends; to determine the parameters of these trends spectral estimation methods, such as periodograms, correlograms, fast Fourier transform, etc., are used. The main shortcoming of these methods is long computational time, especially for the periodogram technique. The amount of calculations can be lowered if some a priori information on the frequency of a harmonic trend, which can be obtained using an easily executed rough frequency analysis, is available.Attention should be drawn to signal analysis in terms of the number of zero crossings (NZC), which can be used for spectral analysis of signals [2]. It is proposed that simple repetitive-difference and repetitive-summing fi lters be used as a fi lter. In the fi rst order, their operation reduces to successive subtraction (addition) of neighboring readouts of the initial data sequence, and application of this operation to the already fi ltered sequence is a second order fi lter, etc. A repetitive-difference fi lter is a high frequency fi lter, while a repetitive-summing fi lter is a low frequency fi lter that is simpler to use and, therefore, takes less computational time, so it can be used in microcontroller devices. In realizing repetitive-difference and -summation fi lters, it should be remembered that the sample volume at the output from the kth order fi lter is k readouts smaller than at the input.Estimating the Frequency of a Periodic Trend. Since NZC methods are associated with the spectral function of the analyzed signal, it is proposed that this fact be used for a rough spectral analysis [3]. To do this, repetitive-difference and -summation fi lters are applied to the signal sequentially in different combinations (the maximum order of fi lters is limited) and the number of zero crossings is calculated for each combination of these fi lters. The set of numbers of zero crossings obtained after applying a series of the simplest fi lters to the signal can be regarded as a sort of spectral function (referred to as a quasispectrum in Ref. 3). It can be used both to estimate the spectrum of the signal being studied, and for other practical tasks, in particular the detection of periodic signals [4]. There is a signifi cant limitation to the quasispectrum; it has low sensitivity at the edges of the frequency band, and this must be ...

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