How do I determine transfer function from input/output data?

I have a discrete-time data set with the following values: u(k)=0 for all k except k=1. When k=1, u(k)=1 (I am basically supplying an impulse signal at one specific time value) y(k)=0 for all k except k=1,2,3. When k=1,2,3 y(k)=1

I need to determine a discrete-time transfer function from this data, and generate a plot of this information. Any pointers would be greatly appreciated.

[Kaushik Lakshminarasimhan]

Why do you need Matlab for this? The transfer function is basically, h(k) = 1 for k = {0, 1, 2} and 0 everywhere else.

[Joe Thompson]

I am trying to learn how to get matlab to generate the information I require. This is why I need Matlab for this. How is the transfer function structured in the way you describe, as there is no input besides an initial impulse at k=0? How would this look in Z-domain?

Answer 1

[Yogananda Jeppu]

If it was filter sort of thing the TF would be available as a X(k+1) = A x(k) + B u(k) form. This would make sense to derive in the Z domain. What you have is what we call as a pulser. If my input changes from 0 -> 1 I send out a pulse for 3 frames.