1.1 Signal power, energy, and frequency

Signals can be characterized in several different ways. Audio signals (music, speech, and really, any kind of sound we can hear) are particularlyuseful because we can use our existing notion of “loudness" and “pitch" which we normally associate with an audio signal to developways of characterizing any kind of signal. In terms of audio signals, we use “power" to characterize the loudness of a sound. Audiosignals which have greater power sound “louder" than signals which have lower power (assuming the pitch of the sounds are within therange of human hearing). Of course, power is related to the amplitude, or size of the signal. We can develop a more precise definition of power. The signal power is definedas:

The energy of this signal is similarly defined

We can see that power has units of energy per unit time. Strictly speaking, the units for energy depend on the units assigned to the signal. If $x\left(t\right)$ is a voltage, than the units for $e_x$ would be volts ${}^2$ -seconds. Notice also that some signals may not have finite energy. As we will see shortly, periodic signals do not have finite energy. Signals having a finite energy are sometimes called energy signals . Some signals that have infinite energy however can have finite power. Such signals are sometimes called power signals .

We use the concept of “frequency" to characterize the pitch of audio signals. The frequency of a signal is closely related to thevariation of the signal with time. Signals which change rapidly with time have higher frequencies than signals which are changing slowlywith time as seen [link] . As we shall see, signals can alsobe represented in terms of their frequencies, $X\left(j\Omega \right)$ , where $\Omega$ is a frequency variable. Devices which enable us to view the frequency content of a signal in real-time are called spectrum analyzers .

Something to keep in mind is that the signals shown in Figures [link] , [link] , and [link] each have different units (degrees Fahrenheit, pressure, and voltage,respectively). So while we can compare relative frequencies betweenthese signals, it doesn't make much sense to compare their power since each signal has different units. We will take a more formallook at the frequency of signals starting in Chapter 2.