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The zero-order hold (ZOH) is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter (DAC). [1] That is, it describes the effect of converting a discrete-time signal to a continuous-time signal by holding each sample value for one sample interval. It has several applications in electrical ...
Commonly used are: zero-order hold (for film/video frames), cubic (for image processing) and windowed sinc function (for audio). The two methods are mathematically identical: picking an interpolation function in the second scheme is equivalent to picking the impulse response of the filter in the first scheme.
Jitter, noise, and quantization are often analyzed by modeling them as random errors added to the sample values. Integration and zero-order hold effects can be analyzed as a form of low-pass filtering. The non-linearities of either ADC or DAC are analyzed by replacing the ideal linear function mapping with a proposed nonlinear function.
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, 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 ...
Another class of reconstruction filters include the Gaussian for various widths, [2] or cardinal B-splines of higher order – the box filter and tent filter being the 0th and 1st order cardinal B-splines. These filters fail to be interpolating filters, since their impulse response do not vanish at all non-zero original sample points – for 1: ...
The Zero-order hold (ZOH) is a mathematical model of the practical reconstruction of sampled signals done by conventional digital-to-analog converters (DAC). When a signal, x(t), is sampled at intervals of length T, we are left with just the discrete sequence : x(nT), for integer values of n.
In order to take advantage of a fast Fourier transform algorithm for computing the DFT, the summation is usually performed over all terms, even though of them are zeros. Therefore, the case L < N {\displaystyle L<N} is often referred to as zero-padding .
A solution to a discretized partial differential equation, obtained with the finite element method. In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical ...