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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 Balian-Low theorem ： ウィキペディア英語版 Balian–Low theorem In mathematics, the Balian–Low theorem in Fourier analysis is named for Roger Balian and Francis E. Low. The theorem states that there is no well-localized window function (or Gabor atom) ''g'' either in time or frequency for an exact Gabor frame (Riesz Basis). Suppose ''g'' is a square-integrable function on the real line, and consider the so-called Gabor system :$g\_(x)\; =\; e^\; g(x\; -\; n\; a),$ for integers ''m'' and ''n'', and ''a,b>0'' satisfying ''ab=1''. The Balian–Low theorem states that if :$\backslash \backslash \}$ is an orthonormal basis for the Hilbert space :$L^2(\backslash mathbb),$ then either :$\backslash int\_^\backslash infty\; x^2\; |\; g(x)|^2\backslash ;\; dx\; =\; \backslash infty\; \backslash quad\; \backslash textrm\; \backslash quad\; \backslash int\_^\backslash infty\; \backslash xi^2|\backslash hat(\backslash xi)|^2\backslash ;\; d\backslash xi\; =\; \backslash infty.$ The Balian–Low theorem has been extended to exact Gabor frames. == See also == * Gabor filter (in image processing) 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「Balian–Low theorem」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.