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

  • $\begingroup$ Please show what work you have done so far and where you are stuck $\endgroup$
    – Hilmar
    Apr 18, 2020 at 17:05
  • $\begingroup$ What is 􀀀 in the question? $\endgroup$
    – lennon310
    Apr 18, 2020 at 18:03

1 Answer 1


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.

  • $\begingroup$ I wasn't able to take online classes due to the pandemic. Can you please help me finish it somehow? $\endgroup$ Apr 18, 2020 at 17:34
  • $\begingroup$ @YaAliCoder Follow this Question and answer and you will get detailed idea : dsp.stackexchange.com/a/66350/49439 $\endgroup$
    – DSP Rookie
    Apr 18, 2020 at 17:53

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