Fast complexified quaternion Fourier transform

被引：66

作者：

Said, Salem ^{[1
]}

Le Bihan, Nicolas ^{[1
]}

Sangwine, Stephen J. ^{[2
]}

机构：

[1] GIPSA Lab, Dept Images & Signal, F-38402 St Martin Dheres, France

[2] Univ Essex, Dept Comp & Elect Syst, Colchester CO4 3SQ, Essex, England

来源：

IEEE TRANSACTIONS ON SIGNAL PROCESSING | 2008年 / 56卷 / 04期

关键词：

biquaternion Fourier transform (BiQFT); biquaternion-valued signals; fast algorithm (BiQFFT); Hermitian symmetries; hyperanalytic signal;

D O I：

10.1109/TSP.2007.910477

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

In this paper, we consider the extension of the Fourier transform to biquaternion-valued signals. We introduce a transform that we call the biquaternion Fourier transform (BiQFT). After giving some general properties of this transform, we Show how it can be used to generalize the notion of analytic signal to complex-valued signals. We introduce the notion of hyperanalytic signal. We also study the Hermitian symmetries of the BiQFT and their relation to the geometric nature of a biquaternion-valued signal. Finally, we present a fast algorithm for the computation of the BiQFT. This algorithm is based on a (complex) change of basis and four standard complex FFTs.

引用

页码：1522 / 1531

页数：10