| Presentation | 2021-03-16 Approximate formula of the mean square quantization error of golden ratio encoders Yoshikatsu Kashiwabara, Yutaka Jitsumatsu, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(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 $. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Golden Ratio Encoder / Analog-to-Digital Conversion / Quantization Error / Two-dimensional Discrete-time Dyamical System |
| Paper # | NLP2020-63 |
| Date of Issue | 2021-03-08 (NLP) |
| Conference Information | |
| Committee | NLP / MSS |
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| Conference Date | 2021/3/15(2days) |
| 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. |
| Chair | Kiyohisa Natsume(Kyushu Inst. of Tech.) / Shigemasa Takai(Osaka Univ.) |
| Vice Chair | Takuji Kosaka(Chukyo Univ.) / Atsuo Ozaki(Osaka Inst. of Tech.) |
| Secretary | Takuji Kosaka(Kyushu Inst. of Tech.) / Atsuo Ozaki(Kagawa Univ.) |
| Assistant | Toshikaza Samura(Yamaguchi Univ.) / Hideyuki Kato(Oita Univ.) / Naoki Hayashi(Osaka Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Nonlinear Problems / Technical Committee on Mathematical Systems Science and its Applications |
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| Language | JPN |
| 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 |
| 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.) |
| Date | 2021-03-16 |
| Paper # | NLP2020-63 |
| Volume (vol) | vol.120 |
| Number (no) | NLP-430 |
| Page | pp.pp.47-52(NLP), |
| #Pages | 6 |
| Date of Issue | 2021-03-08 (NLP) |