# Minimum Energy Delay Property

I have 4 systems which are represented in z domain like this:

Where I know the poles and zeros.

Then I compute Partial Energy Sequence of impulse response of all these system using this formula:

And I get this result:

And I want to observe minimum energy delay property of the minimum phase systems can be specified as:

If I am right, the formula above tells us that minimum phase system has a bigger or equal at least partial energy but, unfortunately, you can see in partial energy sequence plot, the minimum phase system has the smallest partial energy!

Am I interpreting the minimum energy delay formula wrong or what am I missing here?

Given only the zeros and poles, the impulse response is determined except for a constant $K_i$, which you don't show.
If you normalize all filters so that all impulse responses have the same energy (i.e. $\sum_n |h_i[n]|^2$ is the same for the 4 filters), then the 4 curves for partial energies will end up at the same value, and it will be clear that $H_1$ has its energy distributed earlier in time than the others.
• Maybe you are looping with the already updated values? Try a different name for the normalized filters: h2N_n = h2_n/sum(...) May 22, 2015 at 17:03