Time-varying signals are commonly observed in the laboratory as well as many other applied settings. Consider, for example, the voltage level that is present at a specific point in a circuit. In theory, the voltage level can be represented by a real number. More specifically, the voltage level can theoretically be represented by any real number at any instant in time, a feature that conforms to the main characteristics of an analog signal. Suppose that an analog voltage level is measured (sampled) using an oscilloscope (o-scope). The o-scope displays a graph of the voltage level, with time depicted in the horizontal direction (t axis) and voltage level in the vertical direction (y axis). Each (t, y(t)) point on the o-scope graph represents a measurement of the line voltage at the corresponding time when the measurement was made. The o-scope displays the voltage signal in the time domain, i.e., how the voltage varies through time.
As a practical example, suppose a waveform generator is used to create a signal by summing three sinusoids and a noise component. To program the waveform generator, several characteristics of each sinusoid must be entered. A sinusoidal waveform is specified using four critical features: frequency, peak amplitude, phase, and vertical offset. A (simplistic) noise component can be specified by declaring its peak amplitude, with the understanding that the noise values are distributed around zero in some manner, e.g., "random (uniform) noise" has a uniform distribution with zero mean, and "band-limited white noise" has a normal distribution with zero mean (see Section 5.2).