A new method for an almost-on-the-fly estimation of the instantaneous frequency and of the amplitude of a signal

Abstract

The instantaneous frequency (IF) of a signal is a parameter whose estimation is of prime importance in a number of domains ranging from musical acoustics to seismics and astronomy. Its determination is usually based on one of the following three general methods: the derivation of the phase of the associated analytic signal, the Wigner–Ville transform and others Cohen’s class transforms, or the three-point algorithms like the Teager–Kaiser ‘‘energy operator.’’ A new three-point method is described which is simple, fast, precise, robust to noise, and estimates the IF and the amplitude with a very small delay. This method gives excellent results on almost any kind of chirps (polynomials, hyperbolics, exponentials, etc.) and frequency modulations (sinusoidal, FSK, Gaussian pulse, etc.), whether or not associated with amplitude modulation (sinusoidal, Gaussian, etc.). The relative errors on the amplitude and on the IF are usually around 1% in the no-noise case, and increase to about 5% for a 20-dB signal-to-noise ratio, even when these different modulations are associated.