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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 First-order hold ： ウィキペディア英語版 First-order hold The first-order hold (FOH) is a mathematical model of the practical reconstruction of sampled signals that could be done by a conventional digital-to-analog converter (DAC) and an analog circuit called an integrator. For the FOH, the signal is reconstructed as a piecewise linear approximation to the original signal that was sampled. A mathematical model such as the FOH (or, more commonly, the zero-order hold) is necessary because, in the sampling and reconstruction theorem, a sequence of dirac impulses, ''x''s(''t''), representing the discrete samples, ''x''(''nT''), is low-pass filtered to recover the original signal that was sampled, ''x''(''t''). However, outputting a sequence of dirac impulses is decidedly impractical. Devices can be implemented, using a conventional DAC and some linear analog circuitry, to reconstruct the piecewise linear output for either the predictive or delayed FOH. Even though this is not what is physically done, an identical output can be generated by applying the hypothetical sequence of dirac impulses, ''x''s(''t''), to a linear, time-invariant system, otherwise known as a linear filter with such characteristics (which, for an LTI system, are fully described by the impulse response) so that each input impulse results in the correct piecewise linear function in the output. ==Basic first-order hold== The first-order hold is the hypothetical filter or LTI system that converts the ideally sampled signal : \delta(t - nT) \ |- | |$=\; T\; \backslash sum\_^\; x(nT)\; \backslash delta(t\; -\; nT)\; \backslash$ |} to the piecewise linear signal :$x\_^\; x(nT)\; \backslash mathrm\; \backslash left(\backslash frac\; \backslash right)\; \backslash$ resulting in an effective impulse response of : $h\_\; \backslash mathrm\; \backslash left(\backslash frac\; \backslash right)$ = \begin \frac \left( 1 - \frac \right) & \mbox |t| < T \\ 0 & \mbox \end \ : where $\backslash mathrm(x)\; \backslash$ is the triangular function. The effective frequency response is the continuous Fourier transform of the impulse response. : \ \ |- | |$=\; \backslash left(\; \backslash frac\}\; \backslash right)^2\; \backslash$ |- | |$=\; \backslash mathrm^2(fT)\; \backslash$ |} : where $\backslash mathrm(x)\; \backslash$ is the normalized sinc function. The Laplace transform transfer function of the FOH is found by substituting ''s'' = ''i'' 2 π ''f'': : \ \ |- | |$=\; \backslash left(\; \backslash frac\}\; \backslash right)^2\; \backslash$ |} This is an acausal system in that the linear interpolation function moves toward the value of the next sample before such sample is applied to the hypothetical FOH filter. This acausality is also reflected in the impulse response of the FOH filter beginning to respond before impulse is applied. 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「First-order hold」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.