How to interpolate a step function?

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Diemo Schwarz el 29 de Mzo. de 2018

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https://es.mathworks.com/matlabcentral/answers/391414-how-to-interpolate-a-step-function

If I have a function with steps that I want to sample regularly, interp1 complains about not strictly monotonic data. However, a step in the data is being interpreted as being defined up to the next time point, interpolation (at least table lookup) is well defined. How can one achieve this in matlab?