| Generalized sampling expansions associated with quaternion Fourier transform | |
| Cheng D.; Kou K.I. | |
| 2018-07-30 | |
| Source Publication | Mathematical Methods in the Applied Sciences |
| Volume | 41 |
| Issue | 11 |
| Pages | 4021-4032 |
| 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 σ-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 σ-bandlimited quaternion-valued signal in quaternion linear canonical transform sense. Examples are given to illustrate our results. Copyright © 2017 John Wiley & Sons, Ltd. |
| Keyword | convolution theorem generalized sampling expansions generalized translation quaternion Fourier transform quaternion linear canonical transform Quaternion-valued signals |
| DOI | 10.1002/mma.4423 |
| URL | View the original |
| Language | 英語 |
| Fulltext Access | |
| Citation statistics | |
| Document Type | Conference paper |
| Collection | University of Macau |
| Affiliation | Universidade de Macau |
| Recommended Citation GB/T 7714 | Cheng D.,Kou K.I.. Generalized sampling expansions associated with quaternion Fourier transform[C],2018:4021-4032. |
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