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
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
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:
$\displaystyle \frac{T^{2}}{2}\left[\frac{z(z+1)+z(z-1)+0.25\,z(z-1)^{2}}{(z-1)^{3}}\right].$
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