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| Presentation | 2021-03-16 10:45 Approximate formula of the mean square quantization error of golden ratio encoders Yoshikatsu Kashiwabara, Yutaka Jitsumatsu (Kyushu Univ.)  NLP2020-63 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | The Golden Ratio Encoder (GRE) is a type of analog-to-digital (A/D) conversion method. GRE expands the input analog value $ x $ as $x = b_1 phi^{-1} + b_2 phi^{-2} + ldots $, where $phi$ is the golden ratio. The operation of GRE is described by the two-dimensional discrete-time dynamical system $ (u_n, v_n) = T (u_ {n-1}, v_ {n-1}) $. It is known that the absolute value of the quantization error $ | x-hat {x} | $ of GRE decreases exponentially according to the number of digits $ N $. The goal of this study is to give an accurate evaluation of the mean square quantization error (MSQE), which is one of the indicators of A/D converters. However, rigorous evaluation for the finite $ N $ is not easy. Recently, the second author gave a relatively simple formula for the MSQE of the GRE based on the assumption that the distribution of the initial value $ (u_0, v_0) $ follows the invariant density of the map $ T $. However, in reality, the initial probability distribution does not satisfy this assumption. In this paper, we show by a number of numerical calculation examples that the error between this approximation formula and the actual MSQE decreases exponentially with respect to $ N $. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Golden Ratio Encoder / Analog-to-Digital Conversion / Quantization Error / Two-dimensional Discrete-time Dyamical System / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 120, no. 430, NLP2020-63, pp. 47-52, March 2021. | |
| Paper # | NLP2020-63 | |
| Date of Issue | 2021-03-08 (NLP) | |
| ISSN | Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | NLP2020-63 |
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| Conference Information | |
| Committee | NLP MSS |
| Conference Date | 2021-03-15 - 2021-03-16 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Online |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | MSS, NLP, Work In Progress (MSS only), and etc. |
| Paper Information | |
| Registration To | NLP |
| Conference Code | 2021-03-NLP-MSS |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Approximate formula of the mean square quantization error of golden ratio encoders |
| Sub Title (in English) | |
| Keyword(1) | Golden Ratio Encoder |
| Keyword(2) | Analog-to-Digital Conversion |
| Keyword(3) | Quantization Error |
| Keyword(4) | Two-dimensional Discrete-time Dyamical System |
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| Keyword(8) | |
| 1st Author's Name | Yoshikatsu Kashiwabara |
| 1st Author's Affiliation | Kyushu University (Kyushu Univ.) |
| 2nd Author's Name | Yutaka Jitsumatsu |
| 2nd Author's Affiliation | Kyushu University (Kyushu Univ.) |
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| Speaker | Author-1 |
| Date Time | 2021-03-16 10:45:00 |
| Presentation Time | 25 minutes |
| Registration for | NLP |
| Paper # | NLP2020-63 |
| Volume (vol) | vol.120 |
| Number (no) | no.430 |
| Page | pp.47-52 |
| #Pages | 6 |
| Date of Issue | 2021-03-08 (NLP) |
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