# Signals & Systems: Periodic Signal

Discussion in 'Homework Help' started by Star-Wing, Oct 16, 2013.

1. ### Star-Wing Thread Starter New Member

Oct 16, 2013
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0
I read somewhere that all non-periodic signals are Energy signals & periodic signals are power signals.

But then I came across the step function (u(t)) which is also non periodic but it is a power signal.
This made me wonder whether u(t) really is non-periodic? I mean, are all the signals classified as periodic & non-periodic? Is there no exception where the signal belongs to neither?

And can someone explain why u(t) is power signal despite being aperiodic?
Thanks~

2. ### studiot AAC Fanatic!

Nov 9, 2007
5,005
515
Perhaps some more context would help.

I am guessing but the statement may be referring to the fact that power is time derivative of energy. This is power is the (time) rate of change of energy. So if you integrate the power over a period you will obtain the total energy flow. For a periodic waveform this simply means multiplying the power times the time.

3. ### WBahn Moderator

Mar 31, 2012
18,079
4,917
It's not a matter of a simple mapping between periodic/aperiodic and power/energy. If it were, why would we need two sets of terms for the same thing.

Signals can be energy signals, power signals, or neither.

An energy signal is a signal that has finite total energy over all time. "Energy" is a generic definition in this case and is simply the square of the signal. Since a periodic waveform extends to plus and minus infinity in time, there are no bounds on the amount of total energy it contains -- as soon as each period contains non-zero energy, the total energy becomes infinite. But if we look, instead, at average energy per time (or power), then a signal with infinite energy over all time still might have finite power over all time.

If we consider a non-periodic signal with finite duration in time, that signal will have a finite amount of energy over all time provided the signal remains finite (with some exceptions such as impulses that are infinite but have finite area when integrated).