Re: Inverse Z-Transform and/or Long Division

• Subject: [mg2203] Re: Inverse Z-Transform and/or Long Division
• From: wagner at bullwinkle.cs.Colorado.EDU (Dave Wagner)
• Date: Mon, 16 Oct 1995 15:52:33 GMT
• Approved: usenet@wri.com
• Distribution: local
• Newsgroups: wri.mathgroup
• Organization: University of Colorado, Boulder
• Sender: daemon at wri.com ( )

In article <45d28g\$63m at ralph.vnet.net>,
Raymond Anthony Ralph DeGennaro II <degennar at bmsrs.usc.edu> wrote:
>I have a rather nasty Z-Transform of a transfer function that looks like:
>             a0 + a1*z^-1 + a2*z^-2
>   H(z) =    ----------------------
>             b0 + b1*z^-1 + b2*z^-2
>
>where a0, a1, a2, b0, b1 and b2 are sums/products of a number of
>paramters.  I have access the the Symbolic Toolbox (uses the Maple kernal)
>in Matlab (reasonable experience) and Mathematica (essentially zero
>experience).
>
>Is there an easy way to bring this back into the time domain in either of
>these packages?

There is a Mathematica standard package called DicreteMath`RSolve` that
contains functions for solving recurrence relations. In particular,
the package function SeriesTerm will attempt to invert a z-transform.
This is the first thing to try.  Load the package by typing

Needs["DiscreteMath`RSolve`"]

Type this exactly as shown.  You can then type

?DiscreteMath`RSolve`*

to get the names of all the functions in the package, and type

?SeriesTerm

to find out how to use the SeriesTerm function.  The book "Guide to
Mathematica Standard Packages", which is supposed to be a part of every
copy of Mathematica, will give you some examples of its use.  If you
can't find this book you can order it from WRI for a token sum.  Or you
can download it in the form of a monolithic postscript file from MathSource.

There is also a MathSource package on digital signal processing that was
written by the DSP group at GA Tech.

There is a package that appeared in the Mathematica Journal
in vol. 4 issue 2 called PowerSeries.m.  This package can do some
amazing transform inversions.  You might be able to find the electronic
supplement to this issue of the journal on MathSource in the "periodicals"
directory.

Finally, at the 1995 Mathematica Developer's Conference a few days ago,
Urs Graf presented a package for doing Laplace and Z transforms.  His
e-mail address is gru at isbiel.ch.

In anticipation of your next question, MathSource is an anonymous ftp
site maintained by Wolfram Research: mathsource.wri.com.

Hope this helps,

Dave Wagner
Principia Consulting
(303) 786-8371
dbwagner at princon.com
http://www.princon.com/princon

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