Example 9.16
(a). Use
z-transform
methods to solve
with
.
Explore Solution 9.16(a).
It is worthwhile to point out how Mathematica can do the important step using residues.
![[Graphics:../Images/ZTransformDEMod_gr_237.gif]](../Images/ZTransformDEMod_gr_237.gif)
To solve
with
, we
will use our Mathematica subroutine
for
finding the solution to
. It
will take the z-transforms of each term; solve
for
; and
it's inverse
. The
format of the subroutine call is
with
.
![[Graphics:../Images/ZTransformDEMod_gr_247.gif]](../Images/ZTransformDEMod_gr_247.gif)
![[Graphics:../Images/ZTransformDEMod_gr_248.gif]](../Images/ZTransformDEMod_gr_248.gif)
To solve
with
, we
will use our Mathematica subroutine
for
finding the solution to
. It
will take the z-transforms of each term; solve
for
; and
it's inverse
. The
format of the subroutine call is
with
.
![[Graphics:../Images/ZTransformDEMod_gr_258.gif]](../Images/ZTransformDEMod_gr_258.gif)
![[Graphics:../Images/ZTransformDEMod_gr_259.gif]](../Images/ZTransformDEMod_gr_259.gif)
![[Graphics:../Images/ZTransformDEMod_gr_261.gif]](../Images/ZTransformDEMod_gr_261.gif)
![[Graphics:../Images/ZTransformDEMod_gr_262.gif]](../Images/ZTransformDEMod_gr_262.gif)