EMD (version 1.5.9)

hilbertspec: Hilbert Transform and Instantaneous Frequency

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

Value

amplitude

matrix of amplitudes for multiple signals xt

instantfreq

matrix of instantaneous frequencies for multiple signals xt

energy

cumulative energy of multiple signals

Details

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

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

# NOT RUN {
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])
# }