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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 Whittaker–Shannon interpolation formula ： ウィキペディア英語版 Whittaker–Shannon interpolation formula The Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers. The formula dates back to the works of E. Borel in 1898, and E. T. Whittaker in 1915, and was cited from works of J. M. Whittaker in 1935, and in the formulation of the Nyquist–Shannon sampling theorem by Claude Shannon in 1949. It is also commonly called Shannon's interpolation formula and Whittaker's interpolation formula. E. T. Whittaker, who published it in 1915, called it the Cardinal series. ==Definition== Given a sequence of real numbers, ''x''(), the continuous function :$x(t)\; =\; \backslash sum\_^\; x()\; \backslash ,\; \backslash left(\backslash frac\backslash right)\backslash ,$ (where "sinc" denotes the normalized sinc function) has a Fourier transform, ''X''(''f''), whose non-zero values are confined to the region |''f''| ≤ 1/(2''T'').  When parameter ''T'' has units of seconds, the bandlimit, 1/(2''T''), has units of cycles/sec (hertz). When the ''x''() sequence represents time samples, at interval ''T'', of a continuous function, the quantity ''f''''s'' = 1/''T'' is known as the sample rate, and ''f''''s''/2 is the corresponding Nyquist frequency. When the sampled function has a bandlimit, ''B'', less than the Nyquist frequency, ''x''(''t'') is a perfect reconstruction of the original function. (See Sampling theorem.) Otherwise, the frequency components above the Nyquist frequency "fold" into the sub-Nyquist region of ''X''(''f''), resulting in distortion. (See Aliasing.) 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「Whittaker–Shannon interpolation formula」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.