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In this paper we analyze the local and global convergence behavior of sampling series with non-equidistant sampling points for the Paley-Wiener space PWpi1 and sampling patterns that are made of the zeros of sine-type functions. It is proven that the sampling series are locally uniformly convergent if no oversampling is used and globally uniformly convergent if oversampling is used. Furthermore,...
Common methods for the calculation of the spectral factorization rely on an approximation of the given spectral density by a polynomial and a subsequent factorization of this polynomial. It is known that the regularity of the stochastic sequence determines the achievable approximation rate of its spectrum. However, since the approximative polynomial should be factorized, it has to be positive. It...
In this paper we analyze the approximation of the outputs of stable linear time-invariant (LTI) systems T by sampling series that use only the samples of the input signal f. For our analysis we use the Paley-Wiener space of signals with absolutely integrable Fourier transform PWpi1 and consider non-uniform sampling patterns. We completely characterize all stable LTI systems T and sampling patterns...
Spectral factorization, Wiener filtering, and many other important operations in information theory and signal processing can be lead back to a Hilbert transform and a Poisson integral. Whereas the Poisson integral causes generally no problems, the Hilbert transform has a much more complicated behavior. This paper investigates the possibility to calculate the Hilbert transformftilde of a given continuous...
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