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wpfun

Wavelet packet functions

    Description

    wpfun is a wavelet packet analysis function.

    [wpws,x] = wpfun(wname,num) returns the num+1 wavelet packets associated with the wavelet wname on dyadic intervals of length 2–7. The wavelet packets are evaluated on the grid x.

    example

    [wpws,x] = wpfun(wname,num,prec) uses dyadic intervals of length 2prec.

    Examples

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    Specify the db2 wavelet. Obtain the wavelet packets Wn, for n=0,,7, associated with the wavelet.

    wv = "db2";
    n = 7;
    [wpws,x] = wpfun(wv,7);

    Plot the wavelet packets

    tiledlayout(2,4)
    for k=0:n
        nexttile
        plot(x,wpws(k+1,:))
        title("n = "+num2str(k))
    end

    Figure contains 8 axes objects. Axes object 1 with title n = 0 contains an object of type line. Axes object 2 with title n = 1 contains an object of type line. Axes object 3 with title n = 2 contains an object of type line. Axes object 4 with title n = 3 contains an object of type line. Axes object 5 with title n = 4 contains an object of type line. Axes object 6 with title n = 5 contains an object of type line. Axes object 7 with title n = 6 contains an object of type line. Axes object 8 with title n = 7 contains an object of type line.

    Input Arguments

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    Wavelet, specified as a character vector or string scalar. For more information, see wfilters.

    Index, specified as a nonnegative integer. The wpfun function returns num+1 wavelet packets.

    Data Types: double

    Length of the dyadic interval, specified as a positive integer. The length of the interval is 2prec.

    Data Types: double

    Output Arguments

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    Wavelet packets, returned as a matrix. wpws has num+1 rows. The wavelet packets are stored row-wise as [W0; W1; … ; Wnum].

    Grid points where the wavelet packets are evaluated, returned as a real-valued vector.

    More About

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    References

    [1] Coifman, R.R., and M.V. Wickerhauser. “Entropy-Based Algorithms for Best Basis Selection.” IEEE Transactions on Information Theory 38, no. 2 (March 1992): 713–18. https://doi.org/10.1109/18.119732.

    [2] Jaffard, Stéphane, Yves Meyer, and Robert D. Ryan. Wavelets: Tools for Science & Technology. Philadelphia: Society for Industrial and Applied Mathematics, 2001.

    [3] Wickerhauser, M.V. "INRIA lectures on wavelet packet algorithms." Proceedings ondelettes et paquets d'ondes, 17–21 June 1991, Rocquencourt, France, pp. 31–99.

    [4] Wickerhauser, Mladen Victor. Adapted Wavelet Analysis from Theory to Software. Wellesley, MA: A.K. Peters, 1994.

    Version History

    Introduced before R2006a

    See Also

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