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| Computers Forum Index » Computer - DSP » Minimal realization of a LTI system... |
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| chaselweng... |
 Posted: Fri Oct 23, 2009 11:12 am |
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For a given transfer function(matrix) H(z) of a LTI system,
we can employ the Smith-McMillan form to obtain H(z)=A(z)K(z)B(z),
where A(z) and B(z) are unimodulor matrices and K(z) is diagonal
matrix.
The problem is, how can I realize a "minimal" system "directly" from
this Smith-McMillan form.
Minimal means we use minimum number of flip-flops in this system.
I search for a long time on google but still can not find a block
diagram or an example to tell me how to do that.
Could anyone help me to solve this problem....
I think the system looks like:
multiple input ---> [combinational circuit] ---> [flip-flops] ---->
[combinational circuit] ----> multiple output
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| HardySpicer... |
| Posted: Fri Oct 23, 2009 7:33 pm |
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On Oct 23, 4:12 am, chaselweng <jianjiaw... at (no spam) gmail.com> wrote:
Quote: For a given transfer function(matrix) H(z) of a LTI system,
we can employ the Smith-McMillan form to obtain H(z)=A(z)K(z)B(z),
where A(z) and B(z) are unimodulor matrices and K(z) is diagonal
matrix.
The problem is, how can I realize a "minimal" system "directly" from
this Smith-McMillan form.
Minimal means we use minimum number of flip-flops in this system.
I search for a long time on google but still can not find a block
diagram or an example to tell me how to do that.
Could anyone help me to solve this problem....
I think the system looks like:
multiple input ---> [combinational circuit] ---> [flip-flops] ----
[combinational circuit] ----> multiple output
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Do you mean order reduction of a LTI system? Or are you talking of
implementation? |
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| chaselweng... |
| Posted: Sat Oct 24, 2009 3:24 am |
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On Oct 24, 3:33 am, HardySpicer <gyansor... at (no spam) gmail.com> wrote:
Quote: On Oct 23, 4:12 am, chaselweng <jianjiaw... at (no spam) gmail.com> wrote:
For a given transfer function(matrix) H(z) of a LTI system,
we can employ the Smith-McMillan form to obtain H(z)=A(z)K(z)B(z),
where A(z) and B(z) are unimodulor matrices and K(z) is diagonal
matrix.
The problem is, how can I realize a "minimal" system "directly" from
this Smith-McMillan form.
Minimal means we use minimum number of flip-flops in this system.
I search for a long time on google but still can not find a block
diagram or an example to tell me how to do that.
Could anyone help me to solve this problem....
I think the system looks like:
multiple input ---> [combinational circuit] ---> [flip-flops] ----
[combinational circuit] ----> multiple output
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Do you mean order reduction of a LTI system? Or are you talking of
implementation?- Hide quoted text -
- Show quoted text -
I am talking about the implementation based on Smith-McMillan form.
Since from the dominators on the diagonal elements of matrix K(z), we
can know how many memories we really need to realize system. But how
to implement based on the knowledge of A(z), K(z), and B(z). |
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| Tim Wescott... |
| Posted: Sat Oct 24, 2009 5:16 am |
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On Fri, 23 Oct 2009 04:12:42 -0700, chaselweng wrote:
Quote: For a given transfer function(matrix) H(z) of a LTI system, we can
employ the Smith-McMillan form to obtain H(z)=A(z)K(z)B(z), where A(z)
and B(z) are unimodulor matrices and K(z) is diagonal matrix.
The problem is, how can I realize a "minimal" system "directly" from
this Smith-McMillan form.
Minimal means we use minimum number of flip-flops in this system.
I search for a long time on google but still can not find a block
diagram or an example to tell me how to do that. Could anyone help me to
solve this problem....
I think the system looks like:
multiple input ---> [combinational circuit] ---> [flip-flops] ----
[combinational circuit] ----> multiple output
Are you talking about an LTI system over the real numbers, or an LTI
system over some Galois field? 'Cause any system with flip-flops can't
be wholly linear over the real numbers.
I haven't heard of the Smith McMillan form, but after googling around
(and finding your spelling error), a brief look at a couple of papers
tells me that this is more a theoretical tool than a practical one.
What are you _really_ trying to accomplish?
--
www.wescottdesign.com |
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