# Help is required for Z transform

• Jul 7th 2010, 07:18 AM
moonnightingale
Help is required for Z transform
I have to calculate Z transform of following equation

$\displaystyle e^x/s^3$ where x = sT/2 ( I could not write in latex in direct equation thats why i am showing x)

Kindly show me all steps
Thanks
• Jul 7th 2010, 07:45 AM
Ackbeet
Just to clarify, you're required to compute the Z transform of the function $\displaystyle \frac{e^{s T/2}}{s^{3}}$. Is that correct?
• Jul 7th 2010, 07:47 AM
moonnightingale
yes absolutely right
kindly show me all steps to solve this problem
Thanks
• Jul 7th 2010, 07:51 AM
Ackbeet
One more clarification: I'm assuming that $\displaystyle s$ is an integer. Correct?
• Jul 7th 2010, 08:04 AM
moonnightingale
No s is not an integer
s is basically Laplace domain.
Basically this is in continuous time and i have to make it in discrete form for which i have equation
In that equation i have to perform Z transform. of it. then i will move from laplace domain to z domain

Kindly avoid moving from Laplace to time domain and from time domain to z domain
This question is required to be solved directly from Laplace domain to Z domain
Thnnks
• Jul 7th 2010, 08:10 AM
moonnightingale
I am also uploading the solution of instructor but i am unable to understand it

Kindly this to me or if u have got some easy solution that will be more convenient for me
• Jul 7th 2010, 10:03 AM
Ackbeet
I feel like I'm missing something here. Could you please state the original problem, word-for-word? Thanks!
• Jul 8th 2010, 03:11 AM
moonnightingale
Nothing is missing
I just have to find Z transform of this
$\displaystyle e^x/s^3$
where x = sT/2 ( I could not write in latex in direct equation thats why i am showing x)
• Jul 8th 2010, 04:17 AM
CaptainBlack
Quote:

Originally Posted by moonnightingale
I am also uploading the solution of instructor but i am unable to understand it

Kindly this to me or if u have got some easy solution that will be more convenient for me

What you tutor appears to have done is take the inverse LT of G(s)/s, sampled it and then taken the ZT of what resulted (I am assuming that their work is correct).

CB
• Jul 8th 2010, 04:58 AM
Ackbeet
Many thanks to CB for that illuminating post.

There is an error in your tutor's calculations. Everything is correct up until the last line, which should be the following:

$\displaystyle \frac{T^{2}}{2}\left[\frac{z(z+1)+z(z-1)+0.25\,z(z-1)^{2}}{(z-1)^{3}}\right].$
• Jul 8th 2010, 07:02 AM
moonnightingale
I am unable to understand. Can anybody explain this to me with other simple method
Thanks
• Jul 8th 2010, 07:16 AM
Ackbeet
Well, your tutor's method of solution is precisely what CB said it was. That is evidently the method of solution desired. I'm not sure there is a simpler method. The substitution $\displaystyle z=e^{sT}$ does not appear to coincide with your tutor's method. I'm not sure I understand why. Does CB have any ideas?
• Jul 8th 2010, 08:02 PM
CaptainBlack
Quote:

Originally Posted by Ackbeet
Well, your tutor's method of solution is precisely what CB said it was. That is evidently the method of solution desired. I'm not sure there is a simpler method. The substitution $\displaystyle z=e^{sT}$ does not appear to coincide with your tutor's method. I'm not sure I understand why. Does CB have any ideas?

This cannot work for an arbitrary signal as it would imply the equality of a sum dependent on the signal values at the sample points and an integral dependent on the signal at all (positive) times. That these cannot be equal is clear as the value of the integral can be altered by altering the signal between sample points leaving the sum unchanged.

It does map the LT of the signal multiplied by a comb of deltas (iirc) to the ZT of the sampled signal.

CB