We can represent the analytic signal on a plane using a Lissajou curve (a x-y plot). At a given instant, a point on the curve has for its coordinates the values of the signal (horizontal axis) and of the signal in quadrature (vertical axis).

The example shows a signal (top, in blue), whose starting time can be chosen, its signal in quadrature (in black) and the Lissajou curve (in red). Before the starting time the signal is in green. At a given instant, a point on the Lissajou curve turns at a velocity which is a function of the instantaneous frequency. The instantaneous amplitude is shown by a line linking the turning point of the curve to the origin (0,0).

It is possible to study the evolution of the Lissajou curve by modifying the starting instant of the observed blue signal.