A technique for the estimation of fraction-of-time probability density of a digital signal using linear interpolation
T.Ya. Shevgunov · T-Comm - Телекоммуникации и Транспорт · 2024
The paper presents the development of a new tool in fraction-of-time approach, where a random process is described by means of functional models synthesized based on its singe realization, without the need to construct abstract probabilistic models as reliable a priori information on the process ergodicity property is lacking. Based on the analytical formula, expressing the fraction-of-time density of a continuous signal in explicit form, a method for estimating the fraction-of-time density of a digital signal was proposed. A piecewise continuous linear function was chosen as an approximating model used to restore a continuous-time signal from its samples. The first-order interpolating model made it possible to develop a light-weight digital signal processing algorithm that forms an analytical expression for the estimated fraction-of-time density of the observed signal. It is shown that the expression consists of two parts: a regular part rep resented by the sum of rectangle pulses, and a singular part represented by the sum of Dirac deltas. The simulation results are present ed for three cases, including a periodic signal, a stationary random process with its known correlation function, and a second-order cyclostationary process. For the most complex case of a cyclostationary process, the proposed algorithm demonstrated a gain in estimating the probability density compared to the known method of kernel probability density estimation with a Gaussian smoothing function chosen. As an expected direction of practical application of the method and algorithm based on it developed within the framework of the conducted study, an improvement in the quality of solving data analysis problems for which the accuracy of probability density estimates is of significant importance is supposed, for example, problems of detecting random signals with unknown parameters.