Access to eBooks is limited to institutions that have purchased or currently subscribe to the SPIE eBooks program. eBooks are not available via an individual subscription. SPIE books (print and digital) may be purchased individually on SPIE.Org.

Contact your librarian to recommend SPIE eBooks for your organization.
Chapter 6:
2-D Quaternion and Octonion Discrete Fourier Transforms
Abstract
There were many attempts to generalize the known concept of the 2-D DFT, including the 2-D quaternion discrete Fourier transform tailored to color images. The two-side quaternion discrete Fourier transformation (QDFT) was introduced in [1] for the analysis of 2-D linear time-invariant partial-differential systems. The classical fast algorithms are based on representation of the QDFT by a combinations of a few classical DFT transforms. This allows us to obtain QDFT fast numerical implementation with the standard FFT algorithms. In this chapter, we first describe the concept of the 2-D DFT and then the two-side, right, and left-side QDFTs with MATLAB®-based scripts. We start with the effective tensor transform-based algorithm that reduces the 2-D DFT transform to calculation of the separate 1-D DFTs. Then, we describe the 2-D QDFTs, which include the tensor algorithm for calculating the 2-D QDFT and 2-D octonion DFT (ODFT).
Online access to SPIE eBooks is limited to subscribing institutions.
CHAPTER 6
82 PAGES


SHARE
Back to Top