Periodic Signals

Periodic Signals


Periodic signals are more commonly identified by their frequency (usually abbreviated as f ), rather than their period. The frequency of a signal is the inverse of the period. Mathematically, this means that:

\[f = \frac{1}{T}\]

The frequency of a signal tells us how many times the signal repeats itself during one second. Units of frequency are in cycles per second, or Hertz (abbreviated as Hz). Therefore, a signal with a frequency of 100Hz goes through 100 cycles (periods) in one second—the period of the signal is 0.01 seconds. Higher frequency signals change more rapidly, and have shorter periods than lower frequency signals.

Figure 1. Periodic signal. The period of the signal is “T”.

Although any repetitious signal is periodic, there are a few specific signals which are very commonly used in the analysis and testing of electrical circuits. Three examples of common voltage signals are shown in Fig. 2. Periodic voltages are typically classified according to:

  1. Their overall shape (e.g. “sinusoidal”, “triangular”, or “square” in Fig. 2).
  2. Their frequency (the inverse of the periods indicated in Fig. 2).
  3. Their amplitude, or the “height” of the signal, (e.g. “A”, in Fig. 2).

Figure 2. (a) Sinusoidal wave.
Figure 2. (b) Triangular wave.
Figure 2. (c) Square wave.

Figure 2. Basic signal shapes.

The voltage signals in Fig. 2 all have zero average values—they are vertically “centered” around zero volts. We can shift all of these signals vertically by adding a constant value to the time-varying signal—this constant value is called an offset. Most waveform generators provide the ability to add an offset to a basic time-varying signal.

Important Points

  • Periodic signals repeat themselves at a specific time interval. This interval is called the period of the signal.
  • The period of a signal is generally not used in specifying the signal. It is more common to use frequency, which is the inverse of period. The frequency of the signal tells how many periods of the signal occur within one second—the higher the frequency, the more rapidly the signal is changing.
  • Time varying signals are generally categorized by overall shape, frequency, amplitude, and offset. The frequency, amplitude, and offset are indicated on Fig. 3 below for a square wave.
Figure 3. Frequency, amplitude, and offset of a square wave.

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