The Construction of an Orthogonal Complex Wavelet Transform with the Fast Fourier Transform Based on the Perfect Translation Invariance Theorem(Theory)
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- Toda Hiroshi
- Toyohashi University of Technology
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- Zhang Zhong
- Toyohashi University of Technology
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- Imamura Takashi
- Toyohashi University of Technology
Bibliographic Information
- Other Title
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- 完全シフト不変定理を基礎に高速フーリエ変換を用いて構築する正規直交複素数ウェーブレット変換(理論)
- 完全シフト不変定理を基礎に高速フーリエ変換を用いて構築する正規直交複素数ウェーブレット変換
- カンゼン シフト フヘン テイリ オ キソ ニ コウソク フーリエ ヘンカン オ モチイテ コウチク スル セイキ チョッコウ フクソスウ ウェーブレット ヘンカン
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Abstract
In this paper, the perfect translation invariance theorem is proved, which gives the condition of the perfect translation invariance for complex discrete wavelet transforms of an arbitrary complex square integrable function. Next, by using this theorem, the existence of an orthogonal complex wavelet basis on the classical Hardy space is confirmed. Finally, by extending the perfect translation invariance theorem to the case of using the discrete Fourier transform, the orthogonal complex wavelet transform with this wavelet basis is approximated by the orthogonal decomposition constructed with the fast Fourier transform.
Journal
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- Transactions of the Japan Society for Industrial and Applied Mathematics
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Transactions of the Japan Society for Industrial and Applied Mathematics 21 (1), 1-24, 2011
The Japan Society for Industrial and Applied Mathematics
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Details 詳細情報について
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- CRID
- 1390282680744126464
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- NII Article ID
- 110008593899
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- NII Book ID
- AN10367166
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- ISSN
- 09172246
- 24240982
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- NDL BIB ID
- 11068846
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- CiNii Articles
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- Abstract License Flag
- Disallowed