Sampling and interpolation for the discrete Hilbert and Kak-Hilbert transforms

TL;DR

This paper develops sampling and interpolation theorems for the discrete Hilbert and Kak-Hilbert transforms in l^2, extending classical results to these specific discrete transforms.

Contribution

It introduces analogs of sampling theorems and Riesz-Boas interpolation formulas tailored for the discrete Hilbert and Kak-Hilbert transforms.

Findings

Established sampling theorems for discrete Hilbert transforms.

Derived interpolation formulas for Kak-Hilbert transforms.

Extended classical harmonic analysis results to discrete transforms.

Abstract

The goal of the paper is to obtain analogs of the sampling theorems and of the Riesz-Boas interpolation formulas which are relevant to the Discrete Hilbert and Kak-Hilbert transforms in $l^{2}$.