Said, S and Le Bihan, N and Sangwine, SJ (2008) Fast Complexified Quaternion Fourier Transform. IEEE Transactions on Signal Processing, 56 (4). pp. 1522-1531. DOI https://doi.org/10.1109/tsp.2007.910477
Said, S and Le Bihan, N and Sangwine, SJ (2008) Fast Complexified Quaternion Fourier Transform. IEEE Transactions on Signal Processing, 56 (4). pp. 1522-1531. DOI https://doi.org/10.1109/tsp.2007.910477
Said, S and Le Bihan, N and Sangwine, SJ (2008) Fast Complexified Quaternion Fourier Transform. IEEE Transactions on Signal Processing, 56 (4). pp. 1522-1531. DOI https://doi.org/10.1109/tsp.2007.910477
Abstract
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. © 2008 IEEE.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | biquaternion Fourier transform (BiQFT); biquaternion-valued signals; fast algorithm (BiQFFT); Hermitian symmetries; hyperanalytic signal |
| Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science |
| Divisions: | Faculty of Science and Health Faculty of Science and Health > Computer Science and Electronic Engineering, School of |
| SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
| Depositing User: | Unnamed user with email elements@essex.ac.uk |
| Date Deposited: | 05 Mar 2013 14:05 |
| Last Modified: | 30 Oct 2024 20:07 |
| URI: | http://repository.essex.ac.uk/id/eprint/5557 |