# [Maxima] z_transforms

Doug Stewart dastew at sympatico.ca
Sat Feb 14 13:15:13 CST 2009

Robert Dodier wrote:
> On 2/14/09, Doug Stewart <dastew at sympatico.ca> wrote:
>
>
>> I see some work was done on Z Transforms in 2007, but I can't find it now.
>>
>>  I am using Maxima 5.13.0 in Ubuntu.
>>
>>  How do I get it to work?
>>
>
> I recently worked on the z-transform stuff again and made some progress.
> I've committed the z_transform.mac program and rtest_z_transform.mac
> test script. You should be able to see them here:
> http://maxima.cvs.sourceforge.net/maxima/maxima/share/contrib
> They will be in the next release (due in April).
>
> random example:
>
> apply_z_transform (z_transform (1 + kron_delta (m, x), m, u));
>  => 1/u^x+u/(u-1)
>
> batch (rtest_z_transform, test);
>  => (... lots o' stuff ...) 24/24 tests passed.
>
>
> Hope this helps. I';ll be glad to hear any comments. There are
> doubtless many more transform rules that can be implemented,
> maybe we can get going on that. By the way, I'll recommend
>
> best
>
> Robert Dodier
>
>
>
Thank You !!!!

here is one example that needs a little polish :-)

with the "-"  in the exponential it doesn't work

(%i77) apply_z_transform (z_transform (a+b*(e^(-p*T))^(m) , m, z));

a z                     1
(%o77)
----- + b z_transform(-------, m, z)

z - 1                   p T m

(e   )
(%i78)

But without the "-" it works.

(%i76) apply_z_transform (z_transform (a+b*(e^(p*T))^(m) , m, z));

b z                       a z
(%o76)
--------      +            -----

p T                  z - 1

z - e
(%i77)

A happy   Doug