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.