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)

Thank you for your time..


1 Answer 1


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.

Note that this method for transforming a continuous-time filter to a discrete-time filter is useless in practice because stability is generally not preserved, and the transformed frequency response may be drastically different from the original response.

  • $\begingroup$ I know that it is not using due to stability problems. But I had the problem that it won't be causal as it was deduced by a non causal equation.. $\endgroup$
    – Ramesh-X
    Feb 13, 2016 at 3:15
  • $\begingroup$ @Ramesh-X: You could add that example to your question, so we can discuss it. $\endgroup$
    – Matt L.
    Feb 13, 2016 at 20:25
  • $\begingroup$ I understood that it won't be a problem for the causality of the system.. Thanks for your help..! $\endgroup$
    – Ramesh-X
    Feb 14, 2016 at 0:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.