Control theory | Signal processing
First-order hold
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 FOH, the signal is reconstructed as a piecewise linear approximation to the original signal that was sampled. A mathematical model such as FOH (or, more commonly, the zero-order hold) 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 impractical. Devices can be implemented, using a conventional DAC and some linear analog circuitry, to reconstruct the piecewise linear output for either 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, xs(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. (Wikipedia).
