(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given a ramp function x(t) = t*heaviside(t) with the known z-transform ( z / (z-1)^2 ).

If the time-domain signal has been delayed by 2 seconds, then sampled with an unknown sampling rate (T). How could I get the z-transform (one-sided) for the discrete signal, for any values of T ?

I guess my question is really how to express that delay in the Z-domain. I have searched a lot and couldn't find any good resources.

2. Relevant equations

original signal : x(t) = t*heaviside(t) - X(z) = z / (z-1)^2

delayed signal: x(t) = (t-2)*heaviside(t-2) - X(z) = ?

3. The attempt at a solution

I have been trying a lot with this problem. The last (and seemingly to me) the closest I've got is :

X(z) = T*( z / (z-1)^2 )*(z^-s)

where :

s = 2/T if T < 1

s = 2*T if 1<= T < 2

s = T if T >= 2

Of course, if s turns out to be a non-integer value, the solution would be wrong.

Any help on that is greatly appreciated.

Regards,

MT

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Z-transform for a signal with an unknown sampling rate

**Physics Forums | Science Articles, Homework Help, Discussion**