Computing Instantaneous Frequency by normalizing Hilbert Transform
Abstract
This invention presents Normalized Amplitude Hilbert Transform (NAHT) and Normalized Hilbert Transform(NHT), both of which are new methods for computing Instantaneous Frequency. This method is designed specifically to circumvent the limitation set by the Bedorsian and Nuttal Theorems, and to provide a sharp local measure of error when the quadrature and the Hilbert Transform do not agree. Motivation for this method is that straightforward application of the Hilbert Transform followed by taking the derivative of the phase-angle as the Instantaneous Frequency (IF) leads to a common mistake made up to this date. In order to make the Hilbert Transform method work, the data has to obey certain restrictions.
- Inventors:
- Issue Date:
- Research Org.:
- United States Of America, National Aeronautics And Space Administration, Washington, DC (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1175374
- Patent Number(s):
- 6901353
- Application Number:
- 10/615,365
- Assignee:
- The United States of America as represented by the Administrator of the National Aeronautics and Space Administration (Washington, DC)
- Patent Classifications (CPCs):
-
G - PHYSICS G06 - COMPUTING G06F - ELECTRIC DIGITAL DATA PROCESSING
- Resource Type:
- Patent
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Huang, Norden E. Computing Instantaneous Frequency by normalizing Hilbert Transform. United States: N. p., 2005.
Web.
Huang, Norden E. Computing Instantaneous Frequency by normalizing Hilbert Transform. United States.
Huang, Norden E. Tue .
"Computing Instantaneous Frequency by normalizing Hilbert Transform". United States. https://www.osti.gov/servlets/purl/1175374.
@article{osti_1175374,
title = {Computing Instantaneous Frequency by normalizing Hilbert Transform},
author = {Huang, Norden E.},
abstractNote = {This invention presents Normalized Amplitude Hilbert Transform (NAHT) and Normalized Hilbert Transform(NHT), both of which are new methods for computing Instantaneous Frequency. This method is designed specifically to circumvent the limitation set by the Bedorsian and Nuttal Theorems, and to provide a sharp local measure of error when the quadrature and the Hilbert Transform do not agree. Motivation for this method is that straightforward application of the Hilbert Transform followed by taking the derivative of the phase-angle as the Instantaneous Frequency (IF) leads to a common mistake made up to this date. In order to make the Hilbert Transform method work, the data has to obey certain restrictions.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue May 31 00:00:00 EDT 2005},
month = {Tue May 31 00:00:00 EDT 2005}
}
Works referenced in this record:
The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
journal, March 1998
- Huang, Norden E.; Shen, Zheng; Long, Steven R.
- Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 454, Issue 1971