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It seems that sampling requires a numerical representation of the signal. If the numerical representation of a signal is hard to find or not unique, are there any ways to fix this?


Are the functions (e.g., piecewise constant, or linear) chosen dynamically when doing for specific models, or ahead of time depending on assumptions made?


Are there better methods than linear interpolation for reconstruction or is it best to stick with linear interpolation and just increase the number of samples to get better reconstructed results?