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I have $x(t)-> LTI -> y(t)$ where $LTI=h(t),H(jw)$.

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$H(jw)=ab/((a+jw)(b+jw))$ where a and B are real numbers.

I am wanting to find the impulse response $h(t)$ as well as the input/output differential equation to the system.

If my understanding is correct I would want to take the Fourier transform of the frequency response/input and I am not sure where to go from there.

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  • $\begingroup$ Please write a better title. The topic of this whole site is signals and systems. Your title must be more specific to your problem. $\endgroup$
    – Marcus Müller
    Commented Oct 18, 2018 at 18:55
  • $\begingroup$ Okay. I'll update. First time posting. $\endgroup$
    – Kalrondo
    Commented Oct 18, 2018 at 19:23

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$$H(jw) = \frac{output}{input} = \frac{Y(jw)}{X(jw)}$$

$$\frac{Y(s)}{X(s)} = \frac{ab}{(a+s)(b+s)}$$

$$s=jw$$

Then you can use some of the notions from this example to solve for your impulse response / differential equation. Hope that helps!

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  • $\begingroup$ I assume I could also take the inverse Laplace in order to find h(t) correct? $\endgroup$
    – Kalrondo
    Commented Oct 18, 2018 at 19:02
  • $\begingroup$ Correct. the inverse laplace of H(s) will give you h(t). $\endgroup$
    – SignalProcessingJobs
    Commented Oct 18, 2018 at 19:57

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