Generalized sinc Functions from Rational Functions and Applications in Signals

Authors

https://doi.org/10.48314/isti.vi.54

Abstract

The classical Shannon sampling theorem applies exclusively to bandlimited signals. This paper extends the theory to a class of non-bandlimited signals that still permit exact uniform sampling. We introduce a ladder-shaped filter with m real parameters, whose impulse response is a generalized Sinc function obtained from finite Blaschke products. For the corresponding signal space, we establish a generalized sampling theorem that reconstructs any signal from its samples {f(nπ/Ω)}n∈Z using the multi-parameter generalized Sinc kernel. Additionally, we prove that these signals can be analytically extended to a strip in the complex plane, generalizing the Paley–Wiener theorem to the non-bandlimited setting. The proposed framework bridges the gap between classical bandlimited theory and practical non-bandlimited signals, providing both theoretical foundations and tools for signal processing applications.

Keywords:

Shannon sampling, Generalized sinc function, Blaschke product, Ladder shaped filter

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Published

2025-12-07

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Vol. 2 No. 4 (2025): Information Sciences and Technological Innovations

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How to Cite

Niu, S. (2025). Generalized sinc Functions from Rational Functions and Applications in Signals. Information Sciences and Technological Innovations, 2(4), 275-287. https://doi.org/10.48314/isti.vi.54