Standard Article

Hilbert Transform, Envelope, Instantaneous Phase, and Frequency

Signal Processing

  1. Michael Feldman

Published Online: 15 SEP 2009

DOI: 10.1002/9780470061626.shm046

Encyclopedia of Structural Health Monitoring

Encyclopedia of Structural Health Monitoring

How to Cite

Feldman, M. 2009. Hilbert Transform, Envelope, Instantaneous Phase, and Frequency. Encyclopedia of Structural Health Monitoring. .

Author Information

  1. Technion–Israel Institute of Technology, Haifa, Israel

Publication History

  1. Published Online: 15 SEP 2009

Abstract

The application of the Hilbert transform to the signal analysis provides some additional information about amplitude, instantaneous phase, and frequency of vibrations. The Hilbert transform decomposition methods are intended for extracting simple components using the varying instantaneous frequency and amplitude from multicomponent nonstationary signals. The corresponding identification methods directly extract the backbone and damping curve of nonlinear vibration systems. This enables us to solve an inverse identification problem, namely, the problem of estimation of the initial nonlinear static elastic and damping force characteristics.

Keywords:

  • Hilbert transform;
  • analytic signal;
  • envelope;
  • instantaneous phase;
  • instantaneous frequency;
  • empirical mode decomposition;
  • Hilbert vibration decomposition;
  • nonlinear system identification