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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 Polyphase matrix ： ウィキペディア英語版 Polyphase matrix In signal processing, a polyphase matrix is a matrix whose elements are filter masks. It represents a filter bank as it is used in sub-band coders alias discrete wavelet transforms.〔 〕 If $\backslash scriptstyle\; h,\backslash ,\; g$ are two filters, then one level the traditional wavelet transform maps an input signal $\backslash scriptstyle\; a\_0$ to two output signals $\backslash scriptstyle\; a\_1,\backslash ,\; d\_1$, each of the half length: :$\backslash begin$ a_1 &= (h\cdot a_0) \downarrow 2 \\ d_1 &= (g\cdot a_0) \downarrow 2 \end Note, that the dot means polynomial multiplication; i.e., convolution and $\backslash scriptstyle\backslash downarrow$ means downsampling. If the above formula is implemented directly, you will compute values that are subsequently flushed by the down-sampling. You can avoid their computation by splitting the filters and the signal into even and odd indexed values before the wavelet transformation: :$\backslash begin$ h_} &=& a_0 \downarrow 2 \\ h_} &=& (a_0 \leftarrow 1) \downarrow 2 \end The arrows $\backslash scriptstyle\backslash leftarrow$ and $\backslash scriptstyle\backslash rightarrow$ denote left and right shifting, respectively. They shall have the same precedence like convolution, because they are in fact convolutions with a shifted discrete delta impulse. :$\backslash delta\; =\; (\backslash dots,\; 0,\; 0,\; \backslash underset,\; 0,\; 0,\; \backslash dots)$ The wavelet transformation reformulated to the split filters is: :$\backslash begin$ a_1 &= h_} + h_} \rightarrow 1 \\ d_1 &= g_} + g_} \rightarrow 1 \end This can be written as matrix-vector-multiplication :$\backslash begin$ P &= \begin h_} \rightarrow 1 \\ g_} \rightarrow 1 \end \\ \begin a_1 \\ d_1 \end &= P \cdot \begin a_} \end \end This matrix $\backslash scriptstyle\; P$ is the polyphase matrix. Of course, a polyphase matrix can have any size, it need not to have square shape. That is, the principle scales well to any filterbanks, multiwavelets, wavelet transforms based on fractional refinements. == Properties == The representation of sub-band coding by the polyphase matrix is more than about write simplification. It allows the adaptation of many results from matrix theory and module theory. The following properties are explained for a $\backslash scriptstyle\; 2\; \backslash ,\backslash times\backslash ,\; 2$ matrix, but they scale equally to higher dimensions. 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「Polyphase matrix」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.