Abstract:
In this paper we introduce the continuous quaternion wavelet transform (CQWT). We
express the admissibility condition in terms of the (right-sided) quaternion Fourier transform.
We show that its fundamental properties, such as inner product, norm relation, and
inversion formula, can be established whenever the quaternion wavelets satisfy a particular
admissibility condition. We present several examples of the CQWT. As an application
we derive a Heisenberg type uncertainty principle for these extended wavelets.
