The displacement pattern traced out when two sinusoidally varying quantities are superimposed at right angles to each other. These patterns may be obtained in practice on the screen of a cathode-ray oscilloscope by applying the two signals to the horizontal and vertical deflection plates.

The simplest pattern is a straight line, which occurs when two signals of equal frequency and in phase with each other are superimposed. Much more complicated figures result when the ratio of the frequencies is not a simple one. Typical figures are shown in the diagram for various frequency ratios and phase angles. The patterns can be used for accurate frequency matching of two signals or for identifying the phase relationship of two signals of the same frequency.

Lissajous’ figures