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Note that ideally you would approximate the derivative at time instance $t=nT_s$ by the following central difference quotient: $$\frac{dx(nT_s)}{dt}\approx\frac{x[(n+1)T_s]-x[(n-1)T_s]}{2T_s}\tag{1}$$ Since such a system is non-causal - because you would need to know the signal one time step ahead in order to compute the output - you add a delay of one ...


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