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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 Periodic summation ： ウィキペディア英語版 Periodic summation In signal processing, any periodic function$,\; s\_P(t)$  with period P, can be represented by a summation of an infinite number of instances of an aperiodic function$,\; s(t),$ that are offset by integer multiples of P.  This representation is called periodic summation: :$s\_P(t)\; =\; \backslash sum\_^\backslash infty\; s(t\; +\; nP)\; =\; \backslash sum\_^\backslash infty\; s(t\; -\; nP).$ When  $s\_P(t)$  is alternatively represented as a complex Fourier series, the Fourier coefficients are proportional to the values (or "samples") of the continuous Fourier transform$,\; S(f)\; \backslash \; \backslash stackrel\; \backslash \; \backslash mathcal\backslash ,$  at intervals of 1/P.  That identity is a form of the Poisson summation formula. Similarly, a Fourier series whose coefficients are samples of  $s(t)$  at constant intervals (T) is equivalent to a periodic summation of  $S(f),$  which is known as a discrete-time Fourier transform. The periodic summation of a Dirac delta function is the Dirac comb. Likewise, the periodic summation of an integrable function is its convolution with the Dirac comb. == Quotient space as domain == If a periodic function is represented using the quotient space domain $\backslash mathbb/(P\backslash mathbb)$ then one can write :$\backslash varphi\_P\; :\; \backslash mathbb/(P\backslash mathbb)\; \backslash to\; \backslash mathbb$ :$\backslash varphi\_P(x)\; =\; \backslash sum\_\; s(\backslash tau)$ instead. The arguments of $\backslash varphi\_P$ are equivalence classes of real numbers that share the same fractional part when divided by $P$. 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「Periodic summation」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.