ENERGY AND POWER SIGNALS , Definition , Average Normalized Power , Mathematical Representation

By   November 14, 2019

ENERGY AND POWER SIGNALS
In this article, let us define energy and power signals in detials.
Power signal : Definition
A signal is called as a power signal if its average normalized power is non-zero and finite. It has been observed that almost all the periodic signals are power signals.
Energy signal: Definition
          A signal having a finite non-zero total normalized energy is called as an energy signal. It has been observed that almost all the non-periodic signals defined over a finite period, are energy signals. As these signals are defined over a finite period, they are called as time limited signals.
1.17.1 Average Normalized Power
We know that the average normalized power is given by
Equation
The above definition can be generalized for a complex signal x(t) as under:
Equation                                              ……(1.2)
For a periodic signal, with a period T0, equations (1.1) and (1.2) get modified to,
Equation                                              ……(1.3)
For a complex periodic signal x(t), the average normalized power is given by,
Equation                                              ……(1.4)
1.17.2 Energy : Mathematical Representation
The total normalized energy for a real signal x(t) is given by,
Equation                                              ……(1.5)
However, if the signal is complex then the expression for total normalized energy is given by,
Equation                                              ……(1.6)
These equations indicate that the energy is the area under the x2(t) curve over  hence it is always positive.

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