Instantaneous frequency estimation using Osculating Circle Method

There are many methods able to extract the instantaneous frequencies from a time series for practical applications. Gabor´s method is one of the most popular and simple methods; it calculates the instantaneous phase and amplitude of a signal by using its analytic signal. Gabor´s method first uses Hilbert Transform to make the time series analytical. Then, the instantaneous frequencies are calculated by taking the derivative of unwrapped phase. The limitation of Gabor´s method is that it can only be applied to time series with mono component and near zero mean. For wide band time series, Gabor´s method may produce negative frequencies. In this paper, a new method, the Osculating Circle (OC) Method, is presented. The OC method is based on Gabor´s method but with modified unwrapped phase calculation. This new method can provides accurate instantaneous frequency (IF) and instantaneous amplitude (IA) calculation for most of the cases.