The Quaternion Fourier Number Transform

In this paper, we introduce the quaternion Fourier number transform (QFNT), which corresponds to a quaternionic version of the well-known number-theoretic transform. We derive several theoretical results necessary to define the QFNT and investigate its main properties. Differently from other quaternion transforms, which are defined over Hamilton's quaternions, the QFNT requires considering a quaternion algebra over a finite field. Thus, its computation involves integer arithmetic only, avoiding truncation and rounding-off errors. We give an illustrative example regarding the application of the QFNT to digital color image processing.