# Differentials - Differences: Non causality in the system

I'm still learning DSP and referring to Oppenheim video lectures.

In that lectures, differential difference equation is obtained for IIR filter design, in Lecture 14.

$$\mathcal{L}[\frac{\mathrm d}{\mathrm dx}y_a(t)] = sY_a(S)$$ $$\mathcal{Z}[\frac{y[n+1] - y[n]}{T}] = \frac{z-1}{T}Y(z)$$

And using these two equations, difference equation $z-1=sT$ is obtained.

To calculate the z-transform of the differential, $y(n+1)$ is used. By using that term, are we making our system non-causal..? (As our equation depends on future values)

Replacing the derivative by forward differences is just a way to define a transformation from the $s$-plane to the $z$-plane, and it has nothing to do with the causality of the resulting discrete-time filter. As an exercise you could try to do the same with backward differences.