This function seeks the whitest orthonormal transform of a DWPT. The goal is to segment the normalized frequency interval [0, 1/2] into subintervals such that, within each subinterval, the variability of the (corresponding) spectral density function (SDF) is minimized, i.e., each segment of the SDF is as flat as possible. Given an N-point uniformly sampled time series X, and denoting W(j,n) as the DWPT crystal at level j and (sequency ordered) oscillation index n, this optimization is achieved as follows:
Perform a level J - 2 partial DWPT of X where
By definition, W(0,0)=X. Begin
2 with j=n=0.
Perform a white noise test on the current (parent) crystal: W(j,n). If it passes (or the current crystal is in the last decomposition level) retain the crystal. Otherwise, discard the current parent crystal and perform the white noise test on its children: W(j+1,2n) and W(j+1,2n+1).
2 as many times as necessary until a suitable transform is found.
a vector containing a uniformly-sampled real-valued time series or an
object of class
the number of decomposition levels. This argument is used only if
a numeric value on the interval (0,1)
which qualitatively signifies the fraction of times that the
white noise hypothesis is incorrectly rejected.
a character string denoting the white noise test to use.
a character string denoting the filter type.
list containing the
osc vectors denoting
the level and oscillation index, respectively, of the whitest transform.
D. B. Percival, S. Sardy and A. C. Davison, Wavestrapping Time Series: Adaptive Wavelet-Based Bootstrapping, in W. J. Fitzgerald, R. L. Smith, A. T. Walden and P. C. Young (Eds.), Nonlinear and Nonstationary Signal Processing, Cambridge, England: Cambridge University Press, 2001.
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