1 February 2000 Sampling-interpolation modulation transfer function as the envelope of the interpolated output
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The combined process of sampling and nonideal interpolation in imaging, which is not a shift-invariant process, is formulated in terms of a modulation transfer function (MTFs-i). This function is defined as the average envelope of the interpolated output at the sampling points, where the input is a sinusoid and the averaging is over the phase shift of the input relative to the sampler grid. This quantity can be useful in approximating spatial variant systems with the convenient notation of shift-invariant systems. The MTFs-i is derived as two cascaded MTFs: the first one, MTFs, accounts for the replicas of the sampled input that remains in the interpolated output, and the second, MTFi, corresponds to the attenuation of the original signal by the interpolation filter. Unlike the current assumption that MTFs is always a lowpass function, it is shown that at high frequency it has a distorted highpass characteristic. Following Michelson's definition for the visibility of fringes, an index of performance associated with the spatial variation of the process is suggested.
Abraham Friedenberg, "Sampling-interpolation modulation transfer function as the envelope of the interpolated output," Optical Engineering 39(2), (1 February 2000). https://doi.org/10.1117/1.602391

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