Sampling of bandlimited signals in the offset linear canonical transform domain based on reproducing kernel Hilbert space

Abstract

The offset linear canonical transform (OLCT) has proven to be a novel and effective method in signal processing and optics. Many important properties and results of the OLCT have been well studied and published. In this work, the sampling theorem of the OLCT bandlimited signals based on reproducing kernel Hilbert space has been proposed. First, we show that the bandlimited signals in the OLCT domain form a reproducing kernel Hilbert space. Then, an orthogonal basis for the OLCT bandlimited signals has been obtained based on the reproducing kernel Hilbert space. By using the orthogonal basis, the uniform sampling theory for bandlimited signals associated with the OLCT has been obtained. Furthermore, the nonuniform sampling of the OLCT bandlimited signals also has been attained. Finally, the simulations are provided to prove the usefulness and correctness of the derived results.