Synthesis of Hartley-Gabor Signal Bases with Good Frequency-Time Localization for Digital Telecommunication Applications

To increase the efficiency of digital telecommunication systems using signals with orthogonal multiplexing, a new approach is proposed based on the use of orthogonal multi-point Hartley-Gabor signaling bases with good frequency-temporary localization. The advantages of this approach in comparison with the known ones are substantiated. It is shown that the proposed multi-window bases have the property of invariance to the action of a group of frequency-time shifts. This made it possible to develop an effective operator method for their orthogonalization, which turned out to be much simpler than the well-known matrix algebraic method. To construct a computational orthogonalization algorithm, a new spectral apparatus in the form of the Hartley-Zak orthogonal transform has been developed, which is consistent with the group of frequency-time shifts and is of independent practical interest. Strict analytical expressions describing the entire algorithm for the synthesis of the Hartley-Gabor orthonormal basis are given, and the possibility of its fast computational implementation is substantiated. The results of a computational experiment confirming a good time-frequency localization of the basis functions are presented.