The Hilbert transformation > Hilbert transform and instantaneous frequency

A Hilbert transform can be used to estimate the instantaneous frequency of a signal.
The instantaneous frequency is the derivative in time of the instantaneous phase.
This method is efficient if at a given instant, only one spectral component exists.

The example demonstrates the case of a vibro-seismic signal (in blue) for which it is possible to set the upper frequency, the instantaneous frequency (in red) and the modulus of the spectrum of the vibro-seismic signal (in black).