# Convolution of a signal by itself properties [closed]

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.

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

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• Your question is a little too vague to be answered here, too! – Peter K. Feb 17 '15 at 20:50

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.