The size of a signal indicates the largeness or strength of a signal. Such a measurement must consider not only the signal magnitude, but also signal duration.

Signal size can be measured in two ways: energy and power. Energy is used to measure aperiodic signals, while power is used for periodic signals.

Signal Energy

If we just integrate a signal , the positive and negative areas might cancel each other out. To address this, we define the signal size as the area under . This leads to the equation for signal energy:

Comment

The signal energy as described above does not indicate the actual energy (in the conventional sense) of the signal because the signal energy depends not only on the signal, but also on the load

Signal Power

Signal energy must be finite for it to be a meaningful measure of signal size, and a necessary condition for signal energy to be finite is that when . Otherwise the integral will not converge.

However, another type of signals we are interested in are periodic functions such as , which have infinite energy. In such cases, a more useful measure of signal size is the time-averaged energy, if it exists. This measure is called signal power, and it is defined as follows:

RMS Value

The square root of is the root mean square (RMS) value of .

Examples

Example 1

This signal amplitude when , so we can use signal energy

Example 2

signal size example 2.png This signal amplitude does not when , so we cannot use signal energy. However, it is periodic, so we can use signal power. Since a periodic signal repeats regularly each period, averaging over an infinitely large interval is identical to averaging this quantity over one period (2 seconds in this case).

Reference

  • Linear Systems and Signals, 1.1