Hilbert Transform

Summary

Doc_BoxAlgorithm_HilbertTransform.png
  • Plugin name : Hilbert Transform
  • Version : 1
  • Author : Alison Cellard
  • Company : Inria
  • Short description : Hilbert transform, Phase and Envelope from discrete-time analytic signal using Hilbert
  • Documentation template generation date : Nov 2 2017

Description

Return Hilbert transform, phase and envelope of the input signal using analytic signal computation

This box computes the envelope and the instantaneous phase by performing the Discrete-Time Analytic signal [1] using Hilbert transform (see http://en.wikipedia.org/wiki/Analytic_signal).

The definition of analytic signal :

AnalyticRepresentation.png

With x(t) the input signal, H(x) its Hilbert transform and i the imaginary unit.

For more informations on Hilbert transform and EEG see also : http://www.scholarpedia.org/article/Hilbert_transform_for_brain_waves

[1] Marple, S.L., "Computing the discrete-time analytic signal via FFT," IEEE Transactions on Signal Processing, Vol. 47, No.9 (September 1999), pp.2600-2603.

Inputs

1. Input Signal

The input signal

  • Type identifier : Signal (0x5ba36127, 0x195feae1)

Outputs

1. Hilbert Transform

Return the Hilbert transform (imaginary part of the analytic signal) of the input

  • Type identifier : Signal (0x5ba36127, 0x195feae1)

2. Envelope

Return the envelope signal of the input

  • Type identifier : Signal (0x5ba36127, 0x195feae1)

3. Phase

Return instantaneous phase of the input

  • Type identifier : Signal (0x5ba36127, 0x195feae1)

Examples

Miscellaneous