Signal and System practice problem-2

A signal \displaystyle{x}{\left({t}\right)}={A} \cos{{\left(\omega{t}+\phi\right)}} is

a) an energy signal
b) a power signal
c) an energy as well as a power signal
d) neither an energy nor a power signal

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I think A
I.e an energy signal

I think it is power signal

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It’s a periodic signal and hence a power signal.

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It is periodic signal and bounded in it is energy signal.Every periodic signal is not a energy signal.

I know every periodic signal is not a power signal for example x(t) = tan(t), its NENP signal. Only two possibilities for a periodic signal, either it will be power signal or NENP signal. Periodic signals are never energy signals. Calculate the total energy of the above signal you will get infinite and hence it is not an energy signal. Now calculate average power you will get finite value. So the signal is power signal. However its always good to calculate the average power first if it is finite, the total energy is infinite (Power Signal) and if its zero the total energy is finite (Energy Signal).


B- power signal ( it is periodic )

Its a power signal ie option B