Algorithms for construction of orthogonal well-localized bases

The paper considers an algorithm of the construction of orthogonal Weyl-Heisenberg bases which is based on the singular decomposition of the Gabor basis’s matrix. The obtained basis has a good time-frequency localization, because its initializing function is close to the ideally localized Gaussian function. The sequence of the orthogonality conditions of the bases allows the formulation of a new computationally efficient algorithm of orthogonalization based on the fast Fourier transform. The modeling results confirm the identity of the initializing functions obtained as a result of these two algorithms and the good basis localization. The developed fast algorithm makes it possible to considerably expand the field of possible practical application of such bases, including the telecommunication devices based on the principle of orthogonal frequency-time division multiplexing (OFTDM).