A Novel Instantaneous Frequency Computation Approach for Empirical Mode Decomposition

This paper introduces a new instantaneous frequency computation approach
-Counting Instantaneous Frequency for a general class of signals called simple waves. The classsimple wave contains a wide range of continuous signals for which the concept instantaneous frequency has a perfect physical sense. The concept of
-Counting Instantaneous Frequency also applies to all the discrete data. For all the simple wave signals and the discrete data,
-Counting instantaneous frequency can be computed directly without signal decomposition process. The intrinsic mode functions obtained through empirical mode decomposition belongs to simple wave. So
-Counting instantaneous frequency can be used together with empirical mode decomposition.

Authors:

• Liming Zhang

Keywords:

• Instantaneous frequency
• empirical mode decomposition
• intrinsic mode function.

References:

[1] B. Boashash, Estimating and Interpreting the Instantaneous Frequency of
a Signal - Part 1: Fundamentals. Proceedings of the IEEE. Vol. 80, No. 4,
520-538, 1992.
[2] L. Cohen. Time-Frequency Analysis: Theory and Application. Prentice
Hall, Englewood Cliffs, NJ, 1995.
[3] B. Picinbono. On instantaneous amplitude and phase of signals, IEEE
Transactions on Signal Processing. vol. 45, No. 3, March, 1997, 552-560.
[4] N. Huang; Z. Shen; S. R. Long; M. C. Wu; H. H. Shih; Q. Zheng; N. Yen;
C. C. Tung; H. H. Liu. The empirical mode decomposition and the Hilbert
spectrum for nonlinear and non-stationary time series analysis. Proc. R.
Soc. London, A (1998), 454, 903-995.
[5] D. Gabor, Theory of Communication, Journal of the IEE, vol.93,pp.
429-457, 1946.R. C.
[6] Sharpley; V. Vatchev. Analysis of intrinsic mode functions. Constr.
Approx. 24 (2006) 17~47.
[7] T. Qian;L.M.Zhang;H. Li.Mono-components in Signal Decomposition.
International Journal of Wavelets, Multiresolution and Information
Processing. 2008, Vol. 6 (3). 353-374.
[8] T. Qian, L. Zhang and Z. Li, Algorithm of Adaptive Fourier Transform.
IEEE Transactions on Signal Processing. vol. 59(12),5899-5906,
Dec.,2011.
[9] S. Mallat, A wavelet tour of signal processing, Elsevier Inc. 2009.
[10] P. Dang and T. Qian, Analytic Phyas Derivatives, All=Pass Filters and
Signals pf Minimum Phase. IEEE Transactions on Signal
Processing.Vol.59 (10), 2011, 4708-4718.