Hello everybody.

For the definition of the average power of an aperiodic signal (The formula is attched),I have few points:-

1.What is the period of an aperiodic signal, is it zero or infinity.
2. Should i treat the period when applying the formula as a variable that has no finite number(e.g 2pi...etc)

Thanks.

 

The period of an aperiodic signal is undefined.
For calculation purposes you set the period to the time over which you want to know its average value (i.e. sufficient time to calculate many cycles of the signal).

 

OK, but why for energy signal power is zero. If energy is defined then power should also be defined "not equal to zero".
The only factor that sets power P=E/T to zero, is that time being very large "infinity".
Is that true?and if it's true is it practical(no losses)?

 

For an aperiodic signal, the "period" is infinite and so if you want to categorize the entire signal, you need to do so over all time.

This is where the distinction between "power signals" and "energy signals" comes into play.

For some mathematical tools there are requirements placed on the signals that have to be met in order for the mathematical technique to work -- usually in order to ensure convergence of the result. A common requirement is that some trait of the signal be finite when integrated over all time (or all frequencies). Mathematically, a common requirement is "absolute convergence" which means that the integral over all time of the absolute value of a signal be finite. Absolute convergence is almost the same as requiring that the integral of the square of the integrand be finite since the square has the same effect, sign-wise, as taking the absolute value. and any function that won't be finite absolutely won't be finite using the square. I'm not sure if the converse is true or not, but I think it is in practice.

Since the square of a signal is proportional to the energy in the signal, we call any signal for which the integral of the square over all time is finite an "energy signal".

But this leaves out an important set of signals, namely periodic signals such as sine, for which the energy in the signal grows without bound as the time grows. But these signals are still well enough behaved that many of these mathematical tools can still be used. So a slightly weaker form of convergence can sometimes be used, namely that the average power be finite over all time. These are the so-called "power signals".

So basically there are some analysis methods that you can apply to signals that are neither power signals nor energy signals. There are others that you can apply to signals but only if they are power signals (and all energy signals are power signals since the average power of an energy signal is zero), and yet others that you can apply only if they are energy signals. That's why we make the distinction.