Expansions of functions based on rational orthogonal basis with nonnegative instantaneous frequencies. (English) Zbl 1442.41009

Summary: We consider in this paper expansions of functions based on the rational orthogonal basis for the space of square integrable functions. The basis functions have nonnegative instantaneous frequencies so that the expansions make physical sense. We discuss the almost everywhere convergence of the expansions and develop a fast algorithm for computing the coefficients arising in the expansions by combining the characterization of the coefficients with the fast Fourier transform.


41A45 Approximation by arbitrary linear expressions
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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