How to find H(z) and H(k) from a given causal function Consider the causal function,
$y[k] = 2x[k] - 40x[k - 1] + 10y[k - 1]$  $16y[k - 2]$;
where $y[k]$ is the output and $x[k]$ is the input. Assume that the system is initially at rest.
Please someone help me find $H(z)$ and $H(k)$ from given equation. I have an assignment due to tomorrow
It is a Homework problem, so only Hint will be provided. You need to show some work of your own following the hints.

First of all, take $\mathcal Z$-transform of the equation you have. Take care of the delays in time-domain and apply appropriate property of $\mathcal Z$-transform.

Then, try to get the transfer function $H(z)$ from there.

Once you have $H(z)$, figure out a way to convert $H(z)$ into $H(e^{j\omega})$ and then try to proceed for $H[k]$.

Show your work by making updates in your question and we will be clarify the doubts and be able to help you understand.