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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Second-generation wavelet transform ： ウィキペディア英語版 Second-generation wavelet transform In signal processing, the second-generation wavelet transform (SGWT) is a wavelet transform where the filters (or even the represented wavelets) are not designed explicitly, but the transform consists of the application of the Lifting scheme. Actually, the sequence of lifting steps could be converted to a regular discrete wavelet transform, but this is unnecessary because both design and application is made via the lifting scheme. This means that they are not designed in the frequency domain, as they are usually in the ''classical'' (so to speak ''first generation'') transforms such as the DWT and CWT). The idea of moving away from the Fourier domain was introduced independently by David Donoho and Harten in the early 1990s. == Calculating transform == The input signal $f$ is split into odd $\backslash gamma\; \_1$ and even $\backslash lambda\; \_1$ samples using shifting and downsampling. The detail coefficients $\backslash gamma\; \_2$ are then interpolated using the values of $\backslash gamma\; \_1$ and the ''prediction operator'' on the even values: :$\backslash gamma\; \_2\; =\; \backslash gamma\; \_1\; -\; P(\backslash lambda\; \_1\; )\; \backslash ,$ The next stage (known as the ''updating operator'') alters the approximation coefficients using the detailed ones: :$\backslash lambda\; \_2\; =\; \backslash lambda\; \_1\; +\; U(\backslash gamma\; \_2\; )\; \backslash ,$ The functions prediction operator $P$ and updating operator $U$ effectively define the wavelet used for decomposition. For certain wavelets the lifting steps (interpolating and updating) are repeated several times before the result is produced. The idea can be expanded (as used in the DWT) to create a filter bank with a number of levels. The variable tree used in wavelet packet decomposition can also be used. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Second-generation wavelet transform」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.