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Generalized Sampling Expansions Associated with Quaternion Fourier Transform

Authors
  • Cheng, Dong
  • Kou, Kit Ian
Type
Preprint
Publication Date
Jun 28, 2016
Submission Date
Jun 28, 2016
Identifiers
arXiv ID: 1607.06116
Source
arXiv
License
Yellow
External links

Abstract

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 (QLCT) 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 QLCT sense. Examples are given to illustrate our results.

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