The first-order hold is a mathematical model of the practical reconstruction of sampled signals that could be done by a conventional digital-to-analog converter 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 is necessary because, in the sampling and reconstruction theorem, a sequence of dirac impulses, xs(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.

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