The example shows two synthetic signals. The first signal is a sine (carrier) modulated by a Hanning function (envelope). The second signal is the same as the first but with a phase difference and a delay. The Hilbert transform is used to introduce the phase change. It is possible to choose the values of the delay and the phase change.

The example on the left shows, from top to bottom:

• the carriers of the two signals,
• the envelopes of the two signals,
• the two signals.

We show that the interaction or interspectral energy allows measurement of the delay and phase difference. We recall that the interspectrum is the Fourier transform of the intercorrelation function between 2 signals. The slope of the phase of the interspectrum gives the delay between the signals (delay between two envelopes).
The phase change between the carrier is given by the value of the interspectral phase at the origin (null frequency). The delay and phase change measurements have to be made in the frequency interval where the modulus of the interaction energy is significant.

The example on the right shows, from top to bottom:

• the intercorrelation function (in blue) between 2 signals and its envelope (in black),
• the phase (in black) and the modulus (in red) of the interaction energy.