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I have the following question in my mock exam!

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My Answer:

I can apply the dirac delta to know the impulse response. Or use the transfer function $H(z) = \frac{Y(z)}{X(z)}$. I am not sure about the usage of transfer function since it is defined for discrete LTI systems. Are my arguments correct?

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    $\begingroup$ Why should the concept of transfer function be limited to discrete systems? This is not the case. Here, I think the correct (expected) answer is just this: calculate the transfer function. $\endgroup$
    – Max
    Jun 15, 2022 at 6:56

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@Gunners Assuming that the $t$ variable is continuous then your system is continuous (analog). In which case there is no $H(z)$. As for the question: "What would you do to identify the impulse response?" the answer is actually given in the question itself. The impulse response is the $y(t)$ output when the $x(t)$ input is a time-domain impulse.

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