A Novel Approach for Defining a Hilbert Number Transform

Abstract

In this brief, we introduce a new definition for the Hilbert number transform (HNT). Our approach employs concepts related to trigonometry over finite fields and uses as a starting point a specific definition for the Fourier number transform (FNT); one demonstrates that such an FNT allows to define an HNT which is analogous to the real-valued version of the corresponding transform. Additionally, we present a method to obtain the proposed HNT from the recently proposed steerable Fourier number transform.