I am unable to calculate Z transform of t^2 ( t Square)

Can any body show me step by step method to calculate its Z transform

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- June 18th 2010, 09:27 PMmoonnightingaleHelp for Z transform of t^2
I am unable to calculate Z transform of t^2 ( t Square)

Can any body show me step by step method to calculate its Z transform - June 18th 2010, 11:04 PMCaptainBlack
- June 19th 2010, 12:30 AMchisigma
The [one side] z-transform is usually applicable to a

*discrete*sequence and is defined as...

(1)

According to Z-Transform -- from Wolfram MathWorld, if You have a continous function , its z-transform is the z-tranform of the sequence , where T is the so called 'sampling time'. In your case is so that is...

(2)

Kind regards

- June 19th 2010, 01:45 AMmoonnightingale
yes i know answer but how did u perform last step

Kindly explain how u wrote (z-1)^3 in denominator

I am well conversant with Z transform but this step involves some math series

Kindly explain ur last step - June 19th 2010, 02:33 AMCaptainBlack
You differentiate:

twice and manipulate the results to get the series on the right hand side.

CB - June 19th 2010, 03:16 PMchisigma
In detail You start from the expansion...

, (1)

... and then You derivate (1) and obtain ...

(2)

... so that is...

(3)

Now You derivate (3) and obtain...

(4)

... so that is ...

(5)

... and, replacing with , ...

(6)

Kind regards

- June 20th 2010, 03:57 AMmoonnightingale
Thanks a lot for detailed reply