Filter transformation functions - math help

[Ron Crummett]

Hi -

This might be a bit of a bizarre request on the Octave help line, but it 
is Octave-related and I need help, so...

I am trying to write functions that will perform filter transformations 
on a normalized low-pass filter, similar to MATLAB's lp2lp, lp2hp, etc.  
MATLAB performs all of these transformations in state-space and the code 
is printed on their help pages, so to simply copy the code there would 
be plagiarism.

BUT...the way I see it (and help me if I have vision problems) is that 
if I were to derive the transformations myself, then I could code these 
up and it would be perfectly legal.  For a low-pass to low-pass 
transform, this is pretty easy.  If our normalized low-pass filter has 
state-space form

sX = AX+BU
Y = CX+DU

then we substitute s with s/wo (wo being our new cutoff frequency) and get
sX = woAX+woBU
Y = CX+DU

or, in other words, A and B have been scaled by wo.  Unfortunately, the 
other filter transforms are a bit more tricky and this is where I am 
asking for help.  From what I can tell, most of this will take some 
tricky matrix manipulation that I can't immediately figure out. 

I know that some filter transformation operations are available in 
Octave by different names, but I haven't been able to completely 
understand them and I think that functions like lp2lp would be good in 
Octave.  I do not want this to become a large post if it does not need 
to be, so I ask those who know to contact me privately.

Sorry for the length of the post.  I hope that it will result in 
positive and meaningful contributions to Octave.

Thanks,

-Ron