Suppose I have a digital signal measured with sampling time, $T_s=1$ sec. If I take it's derivative, it will, naturally have $T_s=1$ sec. But what are the implications if I re-sample this derivative to have a lower sampling time, such as $T_s=0.1$ sec?
For example, how is the accuracy or representatives of the derivative influenced by re-sampling?
Answer
As you start from a discrete signal, you are likely to interpolate the derivative at a finer step. The result depends on the combination of your interpolation scheme and your discrete derivative estimation.
Your numerical derivative will probably be more convenient, perhaps smoothed, but not "accurate" with respect to what you would have obtained from a $10$ Hz signal, unless you make assumptions on your original signal.
For instance, you can fit (locally) the signal by continuous functions, differentiate them (with penalities on thier variations), and sample the result.
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