Theoretical and applied aspects of the mathematical apparatus of permutation-masking transformations

Abstract

We develop the mathematical apparatus of permutation-masking transformations (PMTs) of different types, enabling us to assign the full set of possible images to the initial generating function. We study the algebraic, spectral, and autocorrelation properties of these transformations. We substantiate the possibility of constructing complex broadband (in the frequency sense) images based on a simple generating function. We study the action of these transformations on stationary random processes, in particular, noncorrelated ones (of the white noise type). The developed apparatus can be applied in many areas, in particular related with the synthesis of the optimal ensembles of signals for communication and management systems; sounding signals for problems of radio-location and navigation; and coding, masking, and enciphering information; and also optimal signal processing in noisy conditions. We consider a demonstrational model example showing the possibility of raising the resolution and estimating quality of the signal parameters on the base of a modified correlator.