Orthogonality criteria of well-localized bases

The development of orthogonality critera for general well-localized Weyl-Heisenberg basis in the case of conjugate N-symmetrical prototype function is considered. A reduced basis is constructed. This basis is orthogonal in terms of the ordinary scalar product if the Weyl-Heisenberg basis is orthogonal in terms of the real scalar product. Some orthogonality criteria in time and frequency domains are proved for the reduced basis. The numerical results of calculation confirm the adecate localization characteristics and the feasibility of the criteria. These criteria are necessary to constuct a computationally efficient basis construction algorithm. They are also used in signal generation and analysis, in particular, to develop the digital telecommunication systems with orthogonal time frequency multiplexing (OFTDM systems).