TY - JOUR

T1 - On instantaneous frequency

AU - Huang, Norden E.

AU - Wu, Zhaohua

AU - Long, Steven R.

AU - Arnold, Kenneth C.

AU - Chen, Xianyao

AU - Blank, Karin

PY - 2009/4

Y1 - 2009/4

N2 - 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 as 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 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 timefrequency analysis is thus taking another step toward maturity.

AB - 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 as 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 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 timefrequency analysis is thus taking another step toward maturity.

KW - Hilbert transform

KW - Instantaneous frequency

KW - empirical AM/FM decomposition

KW - empirical mode decomposition

KW - normalized intrinsic mode function

KW - quadrature

UR - http://www.scopus.com/inward/record.url?scp=77951668826&partnerID=8YFLogxK

U2 - 10.1142/S1793536909000096

DO - 10.1142/S1793536909000096

M3 - 回顧評介論文

AN - SCOPUS:77951668826

SN - 1793-5369

VL - 1

SP - 177

EP - 229

JO - Advances in Adaptive Data Analysis

JF - Advances in Adaptive Data Analysis

IS - 2

ER -