Abstract
Motivated by the treatment of quaternion Fourier transform (QFT), the main purpose of the present paper is to characterize the spectrum of quaternion-value signals on the quaternion Fourier transform domain. Precisely, we attempt to establish a new uncertainty principle (UP) for the general two-sided QFT using the quaternionic Fourier series representation. This result extends the Benedicks, Amrein and Berthier’s UP, which states that a non-zero function in
L
1
R
2
,
H
and its associated two-sided QFT cannot both have support of a finite measure.