Why is my continuous filter different after I convert to Z domain and then back to S domain?

Altair Forum User

Submitted by Joe on Thu, 11/19/2009 - 05:30 

 

I think is is very cool that I can design a Butterworth, Bessel or Chebychev filter, and choose low pass, high pass, band pass filtering using the filter design wizard in the transfer function block. The resulting filters always seem to work as expected. However, when I convert it to Z domain using the S->Z button, and then convert it back, usually the resulting filter is very different from what I started with and doesn't work well at all. How come?

Altair Forum User

Submitted by Anders89 on Thu, 11/19/2009 - 06:26.

The Tustin (bilinear) transform of a continuous filter to a discrete filter is an approximation. It represents a mapping of the left half of the complex s-plane on to the unit circle. The nice thing about the Tustin transform is that a stable continuous pole maps to a stable Z domain pole. The pole locations will not be exactly equivalent, but if the original continuous filter was stable, the resulting discrete filter will be stable. Likewise the transform from discrete to continuous is also an approximation mapping the unit circle onto the left half complex s-plane. That is why you don't end up where you started when you do an S->Z followed by a Z->S.