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I'm studying for a test and I can't really explain this question very well.

If we convolve a signal by itself, will it have the same properties (time-invariant, linear, stable, casual)?

I know how to prove if the signal has a certain property, but I'm not sure the property is retained if a signal is convolved by itself, for all signals.

I'll appreciate it if someone can explain this concept to me. Thanks in advance.

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closed as unclear what you're asking by lennon310, jojek, Peter K. Feb 17 '15 at 20:50

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Your question is a little too vague to be answered here, too! $\endgroup$ – Peter K. Feb 17 '15 at 20:50
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A signal does not have the properties time-invariant, linear, stable, casual that you wish to ascribe to it; these are properties of systems. Properties of signals that might be of interest include

  • bounded amplitude versus unbounded amplitude
  • discrete amplitude versus continuous amplitude
  • discrete-time versus continuous-time
  • periodic versus nonperiodic
  • finite energy or finite power or neither
  • single frequency versus multi-frequency
  • finite bandwidth versus infinite bandwidth
  • baseband versus passband

and possibly others.

Thus, your question is pretty much unanswerable.

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