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Aug 3 at 13:21 comment added Marcus Müller I can't follow you on this. TI is a constraint on time domain. Your like for looking at it in th e frequency domain is not something that's universally useful. It isn't here, far as I can tell.
Aug 3 at 13:19 comment added R24698 Thank you! I agree with you, I got confused over nothing. I find that looking at things both in time and frequency domains helps me, so after agreeing on the time domain, I want to make sure that my view of the explanation in the frequency domain is correct. As I have said in the question, if we take a system and say that it changes the sampling rate, let's say by L (T'=Ts*L), the output of that system will be $\frac{L}{T_s} \sum_k X\left(j \frac{\omega - 2\pi k}{T_s / L}\right)$, which can't be achieved with an LTI system as $y(e^{j\omega})=x(e^{j\omega})H(e^{j\omega})$. Is this correct?
Aug 3 at 13:01 vote accept R24698
Aug 3 at 12:57 history edited Marcus Müller CC BY-SA 4.0
deleted 2 characters in body
Aug 3 at 12:47 history answered Marcus Müller CC BY-SA 4.0