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In signal processing, any periodic function with period P, can be represented by a summation of an infinite number of instances of an aperiodic function that are offset by integer multiples of P. This representation is called periodic summation: : When is alternatively represented as a complex Fourier series, the Fourier coefficients are proportional to the values (or "samples") of the continuous Fourier transform at intervals of 1/P. That identity is a form of the Poisson summation formula. Similarly, a Fourier series whose coefficients are samples of at constant intervals (T) is equivalent to a periodic summation of 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 then one can write : : instead. The arguments of are equivalence classes of real numbers that share the same fractional part when divided by . 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
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