The maximal overlap discrete wavelet packet transform (MODWPT).

USAGE:

wavMODWPT( x, wavelet = ``s8", n.levels = 3 )

DESCRIPTION:

Given j, n, t are the decomposition level, oscillation index, and time index, respectively, the MODWPT is given by W(j,n,t) = sum(u(n,l) * W( j-1, floor(n/2), t - 2^(j-1) * l mod N ) ) The variable L is the length of the filters defined by u(n,l) = g(l) / sqrt(2) if n mod 4 = 0 or 3; u(n,l) = h(l) / sqrt(2) if n mod 4 = 1 or 2; for l = 0, ..., L-1 where g and h are the scaling filter and wavelet filter, respectively. By definition, W(0,0,t) = X(t) where X is the original time series.

REQUIRED ARGUMENTS:

x
A vector containing a uniformly-sampled real-valued time series.

OPTIONAL ARGUMENTS:

wavelet
A character string denoting the filter type. See wavDaubechies for details. Default: ``s8".
n.levels
The number of decomposition levels. Default: the maximum level at which there exists at least one interior wavelet coefficient.

VALUE:

result
An object of class WaveletPacket.

REFERENCES:

(1) D. B. Percival and A. T. Walden, ``Wavelet Methods for Time Series Analysis'', Cambridge University Press, 2000.

SEE ALSO:

, , , , , , , .

EXAMPLES:

    ## calculate the MODWPT of an electrocardiogram
    ## sequence out to 3 levels using Daubechies least
    ## asymmetric 8-tap filter set
    result <- wavMODWPT( ecg, wavelet = "s8", n.levels = 3 )

    ## plot the transform
    plot( result )

    ## summarize the transform
    summary( result )