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. For wide band time series, Gabor's method may produce negative frequencies. The limitation of Gabor's method is that, in order to avoid resulting with negative frequencies, it can only be applied to time series with mono component and near zero mean. In this paper, a new method that does not generate negative frequencies, 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 provide accurate instantaneous frequency (IF) and instantaneous amplitude (IA) calculation with only positive frequency results. This paper is focused on overcoming the negative frequency encountered in traditional Garbo's method. Although, other important topics such as the noise are not discussed in detail in this paper.
Hsu, Ming-Kuang; Sheu, Jiun-Chyuan; and Hsue, Cesar
"OVERCOMING THE NEGATIVE FREQUENCIES - INSTANTANEOUS FREQUENCY AND AMPLITUDE ESTIMATION USING OSCULATING CIRCLE METHOD,"
Journal of Marine Science and Technology: Vol. 19:
5, Article 7.
Available at: https://jmstt.ntou.edu.tw/journal/vol19/iss5/7