WaveletComp (version 1.0)

WaveletTransform: Morlet wavelet transformation of a time series

Description

It computes the Morlet wavelet transformation of a given time series, subject to criteria concerning: the time and frequency resolution, an (optional) lower and/or upper Fourier period.

The output is further processed by higher-order functions wt, WaveletCoherency and wc, and can be retrieved from analyze.wavelet and analyze.coherency.

The name and layout were inspired by a similar function developed by Huidong Tian and Bernard Cazelles (archived R package WaveletCo).

Usage

WaveletTransform(x, dt = 1, dj = 1/20,  lowerPeriod = 2*dt, upperPeriod = floor(length(x)*dt/3))

Arguments

x

the time series to be analyzed

dt

time resolution, i.e. sampling resolution on time domain. Default: 1.

dj

frequency resolution, i.e. sampling resolution on frequency domain, 1/dj = number of voices per octave. Default: 1/20.

lowerPeriod

lower Fourier period (in time units) for wavelet decomposition. Default: 2*dt.

upperPeriod

upper Fourier period (in time units) for wavelet decomposition. Default: (floor of one third of time series length)*dt.

Value

analyze.wavelet with the following elements:

Wave

complex wavelet transform of the series

Phase

phases

Ampl

amplitudes

Period

the Fourier periods (in time units)

Scale

the scales

Power

wavelet power in the time/frequency domain

nc

number of columns/time steps

nr

number of rows/scales/periods

References

Aguiar-Conraria L., and Soares M.J., 2011. The Continuous Wavelet Transform: A Primer. NIPE Working Paper Series 16/2011.

Carmona R., Hwang W.-L., and Torresani B., 1998. Practical Time Frequency Analysis. Gabor and Wavelet Transforms with an Implementation in S. Academic Press, San Diego.

Cazelles B., Chavez M., Berteaux, D., Menard F., Vik J.O., Jenouvrier S., and Stenseth N.C., 2008. Wavelet analysis of ecological time series. Oecologia 156, 287--304.

Liu Y., Liang X.S., and Weisberg R.H., 2007. Rectification of the Bias in the Wavelet Power Spectrum. Journal of Atmospheric and Oceanic Technology 24, 2093--2102.

Tian, H., and Cazelles, B., 2012. WaveletCo. Available at http://cran.r-project.org/src/contrib/Archive/WaveletCo/, archived April 2013; accessed July 26, 2013.

Torrence C., and Compo G.P., 1998. A practical guide to wavelet analysis. Bulletin of the American Meteorological Society 79 (1), 61--78.

See Also

wt, WaveletCoherency, wc, analyze.wavelet, analyze.coherency