Peter, I've found more on Matched Z transform. Never really heard of it before. I used Butterworth filter on my DSP classes. As you might guess, we use Matlab to create it.
Syntax is very simple and powerful:
Code:
[B,A] = BUTTER(N,Wn) designs an Nth order lowpass digital
Butterworth filter and returns the filter coefficients in length
N+1 vectors B (numerator) and A (denominator). The coefficients
are listed in descending powers of z. The cutoff frequency
Wn must be 0.0 < Wn < 1.0, with 1.0 corresponding to
half the sample rate.
So, for this particular example (T = 0.01 and w = 2*pi)
result would be:
Code:
0.0009447 z^2 + 0.001889 z + 0.0009447
--------------------------------------
z^2 - 1.911 z + 0.915
which is same as if Tustin approximation Z transform is used on continuous transfer function.
At the first glance, Matched Z transform looks better to be used, every zero and pole in "s" domain is mapped to correcponding zero and pole in "z" domain. No new zeros or poles are introduced in the discrete transfer function. Also very handy property of sum of coefficients equals 1 is very helpful for checking.
However, since there is so little about it comparing with "zoh" or "tustin", I must conclude that there must be some drawbacks.
First I notice, it will change the gain, but that can be compensated. So, what's the trick here? Is the frequency response of Matched Butterworth filter worse than Butterworth's with Tustin?
There must be something here, otherwise Matched "z" transform would be general knowledge...
