Quaternion-valued signals along with quaternion Fourier transforms (QFT) provide an effective framework for vector-valued signal and image processing. However, the sampling theory of quaternion-valued signals has not been well developed. In this paper, we present the generalized sampling expansions associated with QFT by using the generalized translation and convolution. We show that a sigma-bandlimited quaternion-valued signal in QFT sense can be reconstructed from the samples of output signals of M linear systems based on QFT. Quaternion linear canonical transform is a generalization of QFT with six parameters. Using the relationship between QFT, we derive the sampling formula for sigma-bandlimited quaternion-valued signal in quaternion linear canonical transform sense. Examples are given to illustrate our results. Copyright (c) 2017 John Wiley & Sons, Ltd.

%8 2018-07-30 %D 2018 %I WILEY %J MATHEMATICAL METHODS IN THE APPLIED SCIENCES %P 4021-4032 %V 41 %@ 0170-4214 %U http://repository.umac.mo/handle/10692/365 %W UM