A signal can be classified to be an energy signal or a power signal. In this page, the aspects related to energy and power signals are presented.
Some signals qualify to be classified as energy signals, whereas some other signals qualify to be classified as power signals. Given a continuous-time signal f(t), the energy contained over a finite time interval is defined as follows.
Equation (3.8) defines the energy contained in the signal over time interval from T1 till T2. On the other hand, equation (3.9) defines the total energy contained in the signal. If the total energy of a signal is a finite non-zero value, then that signal is classified as an energy signal. Typically the signals which are not periodic turns out to be energy signals. For example, a single rectangular pulse and a decaying exponential signal are energy signals.
When a reference to power in a signal is made, it points to the average power. Power is defined as energy per second. For a continuous-time signal, we can obtain an expression for power from equation (3.9).
Most of the periodic signals tend to be power signals. Given the period of a cycle, the power of a periodic signal can be defined by equation (3.11). Equation (3.11) can be used to find the power of a dc signal also. The dc signal is also a power signal. If power of a signal is a finite non-zero value and its energy is infinite, then that signal is classified as a power signal. There are some signals which can be classified neither as power signals nor as energy signals. For example, a ramp signal defined from zero till infinity is neither a power signal nor an energy signal, since both power and energy of ramp signal is not bounded. But in practice. such a signal cannot exist and hence such a signal is not of any practical importance.
Example 1:
Given an exponential signal as defined by equation (3.12), find its energy.
Solution:
The solution is expressed by equation (3.13). An exponential signal is an energy signal, since its energy is a finite, non-zero value.
Example 2
Given a sinusoidal signal as defined by equation (3.14), find its power.
Solution:
The solution is expressed by equation (3.15). A sinusoidal signal is a power signal, since the its power over a cycle is a finite, non-zero value. The energy associated with the sinusoidal signal is infinite.
Example 3
Given a square-wave signal as defined by equation (3.15), find its power.
Solution:
The solution is expressed by equation (3.18). A periodic square-wave signal is a power signal, since the its power over a cycle is a finite, non-zero value. The energy associated with the square-wave signal is infinite.
This page has described how a signal qualifies to be either an energy signal or a power signal. The next page is on exponential signal.