Paper Info
Title
Fast Complexified Quaternion Fourier Transform
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.
Year
DOI
Venue
2008
10.1109/TSP.2007.910477
IEEE Transactions on Signal Processing
Keywords
Field
DocType
biquaternion-valued signal,fast complexified quaternion fourier,standard complex ffts,fast algorithm,general property,hermitian symmetry,analytic signal,geometric nature,complex-valued signal,hyperanalytic signal,fourier transforms,magnetic fields,fourier transform,algebra,helium,electromagnetic fields,quaternions,signal analysis,signal processing
Non-uniform discrete Fourier transform,Constant Q transform,Harmonic wavelet transform,Algebra,Short-time Fourier transform,Discrete Fourier transform (general),Hartley transform,Discrete Fourier transform,Fractional Fourier transform,Mathematics
Journal
Volume
Issue
ISSN
56
4
IEEE Transactions on Signal Processing, 56, (4), April 2008, 1522-1531
Citations 
PageRank 
References 
29
1.88
9
Authors
3
Name
Order
Citations
PageRank
S. Said1291.88
N. Le Bihan216510.16
S.J. Sangwine31079.87