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Multiplication and convolution of distributions for signal processing theory
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| Title: | Multiplication and convolution of distributions for signal processing theory |
| Authors: | Akita, Dai Browse this author |
| Keywords: | Theory of signal processing | | Multiplication of distributions | | Convolution of distributions | | Tempered distributions | | LTI systems |
| Issue Date: | Sep-2016 |
| Publisher: | Elsevier |
| Journal Title: | Digital signal processing |
| Volume: | 56 |
| Start Page: | 1 |
| End Page: | 14 |
| Publisher DOI: | 10.1016/j.dsp.2016.05.008 |
| Abstract: | In the theory of signal processing, signals are usually classified either by determining whether their time domain is discrete or continuous, or by determining whether they are periodic. However, no comprehensive definitions of multiplication and convolution exist that are consistent with the theories behind all classes, although some important theorems in signal processing involve multiplication and convolution. In order to unite the theories behind these classifications, we will consider tempered distributions. In this paper, we propose an approach to the multiplication and convolution of distributions that is appropriate to signal processing theory, and prove a well-known theorem regarding the impulse response of continuous linear time-invariant systems of tempered distributions in the context of this new approach. |
| Rights: | © <2016>. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ | | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/70881 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 秋田 大
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