ON INSTANTANEOUS FREQUENCY
Advances in Adaptive Data Analysis
Instantaneous frequency (IF) is necessary for understanding the detailed mechanisms for nonlinear and nonstationary processes. Historically, IF was computed from analytic signal (AS) through the Hilbert transform. This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing IF. The first approach is to compute the quadrature (defined here as a simple 90 • shift of phase angle) directly. The second approach is designated
... the normalized Hilbert transform (NHT), which consists of applying the Hilbert transform to the empirically determined FM signals. Additionally, we have also introduced alternative methods to compute local frequency, the generalized zero-crossing (GZC), and the teager energy operator (TEO) methods. Through careful comparisons, we found that the NHT and direct quadrature gave the best overall performance. While the TEO method is the most 177 Adv. Adapt. Data Anal. 2009.01:177-229. Downloaded from www.worldscientific.com by 22.214.171.124 on 03/08/13. For personal use only. 178 N. E. Huang et al. localized, it is limited to data from linear processes, the GZC method is the most robust and accurate although limited to the mean frequency over a quarter wavelength of temporal resolution. With these results, we believe most of the problems associated with the IF determination are resolved, and a true time-frequency analysis is thus taking another step toward maturity.