Classification of Signals - Signal Processing of Random Physiological Signals - page 14

3.1.3 Energy Signals vs. Power Signals
Is the signal an energy signal or a power signal? Since we are most familiar with
electrical measurements, let us recall that most electrical signals are voltages or currents.
The energy dissipated by a voltage in a resistor for a given period of time is given
by (3.4).

t 2

v 2 ( t )
R

= watt seconds (3.4)

E dt

t 1

Similarly for current, the equation is given in (3.5):

t 2

Ri 2 dt E = (3.5)

t 1

In either equation, the energy is proportional to the integral of the square of the signal.
If the resistance ( R ) is made unity ( R is set at 1 ohm: 1 ), then (3.4) and (3.5) may be

written in the more generalized form as shown in (3.6).

+∞

x 2 ( t ) dt E = < ∞ (3.6)

−∞

Thus (3.4) is used to define an energy signal of infinite energy. An exponentially damped
sinusoid is an example of an energy signal.
What is a power signal? Average power is also known as a “Power Signal.” If
the resistance is assumed to be 1 , then the equation for a power signal is given

by (3.7).

t 2

1

x 2 ( t ) dt P = (3.7)

t 2 − t 1

t 1

From (3.7), one may conclude that the “Power” signal is the energy of a signal in a
time interval divided by the time interval, or restated: Power is the average energy in an
interval of time.