Generalizing the sampling theorem for a frequency-time domain to sample signals under the conditions of a priori uncertainty - Kaliuzhnyi, Mykola (Eastern-European Journal of Enterprise Technologies, 2021)
The radio monitoring of radiation and interference with electronic means is characterized by the issue related to the structural-parametric a priori uncertainty about the type and parameters of the ensemble of signals by radio-emitting sources. Given this, it is a relevant task to devise a technique for the mathematical notation of signals in order to implement their processing, overcoming their a priori uncertainty in terms of form and parameters. A given problem has been solved by the method of generalization and proof for the finite signals of the Whittaker-Kotelnikov-Shannon sampling theorem (WKS) in the frequency-time domain. The result of proving it is a new discrete frequency-temporal description of an arbitrary finite signal in the form of expansion into a double series on the orthogonal functions such as sinx/x, or rectangular Woodward strobe functions, with an explicit form of the phase-frequency-temporal modulation function. The properties of the sampling theorem in the frequency-time domain have been substantiated. These properties establish that the basis of the frequency-time representation is orthogonal, the accuracy of approximation by the basic functions sinx/x and rectangular Woodward strobe functions are the same, and correspond to the accuracy of the UCS theorem approximation, while the number of reference points of an arbitrary, limited in the width of the spectrum and duration, signal, now taken by frequency and time, is determined by the signal base. The devised description of signals in the frequency-time domain has been experimentally investigated using the detection-recovery of continuous, simple pulse, and linear-frequency-modulated (LFM) radio signals. The constructive nature of the resulting description has been confirmed, which is important and useful when devising methods, procedures, and algorithms for processing signals under the conditions of structural-parametric a priori uncertainty.