This toolbox provides different algorithms to analyze the wavelet spectra of time series signals and the wavelet coherence for wavelet spectra.
Functions:
CWT.m
WCO.m
surrogates.m
cardiac_test.m
CWT
The CWT.m provides the continuous wavelet transformation([1],2.4) of a single time series or a matrix of multiple time series. The function supports two different types of wavetlets: the generalized morse wavelet(gmw)([1],2.9.2) and the morlet wavelet([1],2.9.1). The implementation relies mainly on the Matlab cwt.m fuction as well as the the JWavelet module of JLab toolbox.
- supports different wavelets (gmw, morlet wavelet)
- wavelet parametization
- wavelet normalization options
- supports frequency space in scale or period length
- different calculation of the frequency resolution
- supports real as well as imaginary time series
- input of single as well as multiple time series
- calculate the cone of influence (coi)
- plot the wavelet spectrum as well as the time series, coi and space of interest (area between two white lines)
- plot the mother wavelet
- returns the heisenberg area, radius(standard deviation) in time and frequency space of the gmw
Features:
WCO
The WCO.m provides the wavelet coherence([2],2.4) of two wavelet spectra. The shannon entropy([3],pg.956) and phase locking value([4],pg.7) of the wavelet coherence can also be calculated by this function. The implementation relies mainly on the wavelet coherence toolbox by Aslak Grinsted, the ASToolbox, and the WCOH toolbox by Cohen[5].
Features:
- support first order wavelets as well as higher-ordered multiwavelet
- option for output real wavelet coherence or complex wavelet coherence
- smoothing parametization
- support different smoothing algirithm
- plot the wavelet coherence spectrum as well as the time series, coi and space of interest(area between the white lines)
- returns the wavelet coherence, phase locking value and shannon entropy
surrogates
The surrogates.m provides surrogate time series through iterative amplitude adjusted wavelet transform.
Features:
- supports different surrogate algorithm
- iterations parametization
- supports multiple numbers of surrogates
Cardiac_test
the cardiac_test.m evluate if the heart rate is detectable in a time series using the power spectral density. If the state = 1 in result, the cardiac oscillation is present.
Features:
- supports time series matrix(multiple time series)
- plot the power spectral density function
- shows mean and sd for different frequency bins (low frequency (lf),respiration, heart rate, high frequency(hf), foi(frequency of interest) and control.
Reference:
[1] Aguiar-Conraria, L. and Soares, M.J. (2010) "The Continuous Wavelet Transform: A Primer", NIPE Working paper
[2] Cazelles, Bernard, et al. "Time-dependent spectral analysis of epidemiological time-series with wavelets." Journal of the Royal Society Interface 4.15(2007):625.
[3] Cazelles, Bernard, and L. Stone. "Detection of imperfect population synchrony in an uncertain world." Journal of Animal Ecology 72.6(2010):953-968.
[4] Bastos, A. M., and J. M. Schoffelen. "A Tutorial Review of Functional Connectivity Analysis Methods and Their Interpretational Pitfalls. " Frontiers in Systems Neuroscience 9.Pt 2(2016):175.
[5] Cohen, Ed A. K. and Andrew T. Walden. "A Statistical Analysis of Morse Wavelet Coherence."IEEE Transactions on Signal Processing 58 (2010): 980-989.