| No | 214219 |
|---|---|
| 標題（和） | Mixed Trigonometric Interpolation Techniques for Fast and Stable Algebraic Phase Unwrapping |
| 標題（英） | Mixed Trigonometric Interpolation Techniques for Fast and Stable Algebraic Phase Unwrapping |
| 研究会名（和） | 回路とシステム, 通信方式, 信号処理 |
| 研究会名（英） | Circuits and Systems, Communication Systems, Signal Processing |
| 開催年月日 | 2012-03-08 |
| 終了年月日 | 2012-03-09 |
| 会議種別コード | 5 |
| 共催団体名（和） | |
| 資料番号 | CAS2011-161, SIP2011-181, CS2011-153 |
| 抄録（和） | The algebraic phase unwrapping was established in 1998 as a rigorous symbolic algebraic solution to the phase unwrapping problem, i.e., the problem of computing the continuous phase function of a given complex polynomial. In this paper, we propose a simple but a powerful numerical stabilization technique named {\\it the mixed trigonometric interpolation} for the algebraic phase unwrapping. This technique is based on replacing a certain set of arithmetic operations in polynomial ring by an interpolation of a certain mixed trigonometric function. By this technique we can obtain numerical stable approximation of {\\it general Sturm sequence} without suffering the coefficient growth. Moreover, by combining {\\it the mixed trigonometric interpolation} with FFT, we succeeded in making {\\it the mixed trigonometric interpolation} faster and more stable. The proposed techniques allow us to solve phase unwrapping problem along the unit circle stably even if the degree of a given polynomial is very large. |
| 抄録（英） | The algebraic phase unwrapping was established in 1998 as a rigorous symbolic algebraic solution to the phase unwrapping problem, i.e., the problem of computing the continuous phase function of a given complex polynomial. In this paper, we propose a simple but a powerful numerical stabilization technique named {\\it the mixed trigonometric interpolation} for the algebraic phase unwrapping. This technique is based on replacing a certain set of arithmetic operations in polynomial ring by an interpolation of a certain mixed trigonometric function. By this technique we can obtain numerical stable approximation of {\\it general Sturm sequence} without suffering the coefficient growth. Moreover, by combining {\\it the mixed trigonometric interpolation} with FFT, we succeeded in making {\\it the mixed trigonometric interpolation} faster and more stable. The proposed techniques allow us to solve phase unwrapping problem along the unit circle stably even if the degree of a given polynomial is very large. |
| 収録資料名（和） | 電子情報通信学会技術研究報告 |
| 収録資料の巻号 | Vol.111, No.465,466,467 |
| ページ開始 | 303 |
| ページ終了 | 307 |
| キーワード（和） | |
| キーワード（英） | Algebraic phase unwrapping,Numerical stabilization,Coefficient growth,General Sturm sequence,Mixed trigonometric interpolation,FFT |
| 本文の言語 | ENG |
| 著者（和） | 北原大地 |
| 著者（ヨミ） | キタハラ ダイチ |
| 著者（英） | Daichi Kitahara |
| 所属機関（和） | 東京工業大学 |
| 所属機関（英） | Tokyo Institute of Technology |
| 著者（和） | 山田功 |
| 著者（ヨミ） | ヤマダ イサオ |
| 著者（英） | Isao Yamada |
| 所属機関（和） | 東京工業大学 |
| 所属機関（英） | Tokyo Institute of Technology |