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#1 2010-12-31 05:51:35

Onyx
Member
Registered: 2009-02-24
Posts: 48

Inverse z-transform

I have a transfer function:

I can't find it in any transform table. Is it possible to use a convolution sum to solve this from inverse z-transforms of its constituent factors? I can't find a way to do it. Thanks

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#2 2010-12-31 06:54:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Inverse z-transform

Hi Onyx;

Looks like a Z transform. You have to use the inverse Z transform on it. The answer is going to involve the unit step function, which is a piecewise function.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2011-01-01 04:42:23

Onyx
Member
Registered: 2009-02-24
Posts: 48

Re: Inverse z-transform

Thanks, I know I need to use inverse z transform, but I can't find anything in a z-transform table, so I'm not sure how to do it.

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#4 2011-01-01 04:47:22

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Inverse z-transform

Hi Onyx;

If you are looking for a method, there are a couple of them ( all of which I have forgotten ) but like a Laplace transform you usually end up using a table of them anyway. I can provide the answer but as I said it involves the Unit step function ( Heaviside function ). It is a discontinuous function. That is the reason it is not in standard tables.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2011-01-01 04:55:24

Onyx
Member
Registered: 2009-02-24
Posts: 48

Re: Inverse z-transform

Well most the tables I have looked at actually do define the inverse transforms in terms of the unit step, and the unit impulse (Kronecker delta) functions, which is expected, since it represents causality of the discrete time systems I'm working with. I think I mayu need partial fractions...

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#6 2011-01-01 04:58:37

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Inverse z-transform

Hi Onyx;

That is one way of putting it into a form that a table will have. Just holler if you need the answer.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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