# 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

• Please show what work you have done so far and where you are stuck – Hilmar Apr 18 '20 at 17:05
• What is 􀀀 in the question? – lennon310 Apr 18 '20 at 18:03

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 $$H[k]$$.