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How should we characterize a non-LTI system? For example we have: $y[n]=x[3n]+x[2n]+x[n]$ which is clearly not LTI. Also, the impulse response will be $h[n]=3\delta[n]$ and if we take the DTFT of this system I believe $H(e^{j\omega})=3$ which is not very intuitive. How can we characterize this system?

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  • $\begingroup$ A non-LTI system doesn't have an LTI impulse response, so what you conject can't be right. $\endgroup$ – Marcus Müller Apr 6 at 7:10
  • $\begingroup$ You can't characterize a function about which you know literally nothing. You need to first set up a mathematical model of your system, and then you can deduct methods to deduct the parameters of that model. $\endgroup$ – Marcus Müller Apr 6 at 7:11
  • $\begingroup$ @MarcusMüller Thanks for the reply. The only thing I know about this system is that y[n]=x[3n]+x[2n]+x[n]. How can I characterize this system? Is the time-domain equation the only way I can represent this system? $\endgroup$ – Alireza Apr 13 at 21:30
  • $\begingroup$ It's certainly the most useful. You can do whatever math you want to that equation, and call it a representation, as long as the math is correct. But you'll usually not end up with anything useful. $\endgroup$ – Marcus Müller Apr 14 at 7:38

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