hilbertspec: Hilbert Transform and Instantaneous Frequency

In EMD: Empirical Mode Decomposition and Hilbert Spectral Analysis

Description

This function calculates the amplitude and instantaneous frequency using Hilbert transform.

Usage

hilbertspec(xt, tt=NULL, central=FALSE)

Arguments

xt	matrix of multiple signals. Each column represents a signal.
tt	observation index or time index
central	If central=TRUE, use central difference method to calculate the instantaneous frequency

Details

This function calculates the amplitude and instantaneous frequency using Hilbert transform.

Value

amplitude	matrix of amplitudes for multiple signals xt
instantfreq	matrix of instantaneous frequencies for multiple signals xt
energy	cumulative energy of multiple signals

References

Huang, N. E., Shen, Z., Long, S. R., Wu, M. L. Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C. and Liu, H. H. (1998) The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis. Proceedings of the Royal Society London A, 454, 903–995.

Dasios, A., Astin, T. R. and McCann C. (2001) Compressional-wave Q estimation from full-waveform sonic data. Geophysical Prospecting, 49, 353–373.

See Also

spectrogram.

Examples

tt <- seq(0, 0.1, length = 2001)[1:2000]           
f1 <- 1776; f2 <- 1000
xt <- sin(2*pi*f1*tt) * (tt <= 0.033 | tt >= 0.067) + sin(2*pi*f2*tt)
 
### Before treating intermittence
interm1 <- emd(xt, tt, boundary="wave", max.imf=2, plot.imf=FALSE)  
### After treating intermittence
interm2 <- emd(xt, tt, boundary="wave", max.imf=2, plot.imf=FALSE, 
interm=0.0007)

par(mfrow=c(2,1), mar=c(2,2,2,1))
test1 <- hilbertspec(interm1$imf)
spectrogram(test1$amplitude[,1], test1$instantfreq[,1])

test2 <- hilbertspec(interm2$imf, tt=tt)
spectrogram(test2$amplitude[,1], test2$instantfreq[,1])

Example output

Loading required package: fields
Loading required package: spam
Loading required package: dotCall64
Loading required package: grid
Spam version 2.1-1 (2017-07-02) is loaded.
Type 'help( Spam)' or 'demo( spam)' for a short introduction 
and overview of this package.
Help for individual functions is also obtained by adding the
suffix '.spam' to the function name, e.g. 'help( chol.spam)'.

Attaching package: 'spam'

The following objects are masked from 'package:base':

    backsolve, forwardsolve

Loading required package: maps
Loading required package: locfit
locfit 1.5-9.1 	 2013-03-22

EMD documentation built on Jan. 4, 2022, 1:08 a.m.