— The shapes of the Lissajous pattern depends on the frequency and

phase relationship of the two sine waves

— Two sine waves of the same frequency and amplitude may produced a

line, an eclipse or a circle depending on the phase different

2) Frequency Measurement

— to determine frequency by comparing it with the known

frequency

— The unknown frequency (fV ) is presented to the vertical

plate and the known frequency (fh ) is presented to the

horizontal plate

—The more complex the ratio between horizontal and vertical

frequencies, the more complex the Lissajous figure.

When the input to an LTI system is sinusoidal, the output is sinusoidal with the same frequency, but it may have a different amplitude and some phase shift. Using an oscilloscope that can plot one signal against another (as opposed to one signal against time) to plot the output of an LTI system against the input to the LTI system produces an ellipse that is a Lissajous figure for the special case of a = b. The aspect ratio of the resulting ellipse is a function of the phase shift between the input and output, with an aspect ratio of 1 (perfect circle) corresponding to a phase shift of ±90° and an aspect ratio of ∞ (a line) corresponding to a phase shift of 0° or 180°.[citation needed]

The figure below summarizes how the Lissajous figure changes over different phase shifts. The phase shifts are all negative so that delay semantics can be used with a causal LTI system (note that −270° is equivalent to +90°). The arrows show the direction of rotation of the Lissajous figure.