Hello guys,

Very new to this forum but it seems like a good place to learn and share information off of.


I'm taking a signals course this term at my university and was really confused about the definition of power of a signal.

I know that the energy of a signal is the integral from -∞ to +∞ of your signal squared with respect to time. This makes sense to me.


But the power of a signal is defined as the limit as T approaches ∞ of 1/T * the integral of the signal squared from -T/2 to T/2 with respect to time.

what really confuses me is the integral part, i mean your integrating your signal from -∞ to ∞ and essentially dividing by ∞. shoudln't your power always end up being something like ∞/∞. ?????


Idk if you guys could follow this but any help would be appreciated understanding this concept.

 

Sure, and ∞/∞ is indeterminate, but you can find what it limits to, which might be infinity, might be zero, might be some finite nonzero value, or might remain indeterminate.

Consider a pure sinusoid. It has infinite energy because each cycle has energy and there are an infinite number of cycles. But it has finite power because as you double the number of cycles under consideration you also double the time that you are dividing by. Hence the power remains finite.

The reason we care is that there some mathematical things that are only valid on energy signals (i.e., have finite energy over all time) and others that you can also do on power signals (i.e., may have infinite energy over all time, but have finite power).