energy and power basic

in general we are checking whether the signal is power signal or energy signal. What is the use of finding whether the signal is power or energy signal. Do we have any special characteristics for energy and power signal that will be usefull for further analyses.In a nutshell WHY DO WE WANT CARE THE SIGNAL IS POWER OR ENERGY .Thank you in advance

Who is the we in "we are checking........"?
Power is energy per unit time (e.g. 1 watt of power equals 1 joule of energy per second), so the distinction between whether a signal is power or energy makes little sense.
They contain both.

1)All periodic signal are power signal but all power need not to be periodic signal . We have familiar example step signal.but i cant agree with that see my below derivation(attached file) and correct me

2)all non periodic signal are energy signals but vice versa is not true. could you give me an example for this .

signal cannot be both energy and power at the same time ,why?. Need justification.

Look at this Googled definition.
https://www.diffen.com/difference/Energy_vs_Power

I have merged these three threads as it is the same topic.... There really is no need for three threads...

Hello,

You are looking for the "energetic classification" of signals. Lookup the following concepts:
- Finite energy signals.
- Finite average power signals.

A signal can have infinite energy, but a finite average power (check your second equation for power of the Heaviside step (Is the limit of infinity/infinity really infinity, or is it something else?).

Also, check the way you defined u(t). Are you trying to define a gate/boxcar or a "true" Heaviside function (i.e : 0 ; t < 0 and 1 ; t > 0 ). Either way, your integral disagrees with your function.

Try to write your equations in a symbolic way first, then the numbers.