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blscalf

Best-localized Daubechies scaling filter

Since R2022b

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    Syntax

    scalf = blscalf(wname)

    Description

    scalf = blscalf(wname) returns the best-localized Daubechies scaling filter corresponding to wname.

    example

    Examples

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    Open Live Script

    Obtain the scaling filter corresponding to the best-localized Daubechies wavelet with 10 vanishing moments. Confirm the sum of the filter coefficients nearly equals 2 and the L2 norm of the filter nearly equals 1.

    scalf = blscalf("bl10");
sum(scalf)-sqrt(2)
    ans = 
-2.2204e-16

    norm(scalf,2)
    ans = 
1.0000

    Use orthfilt to obtain the scaling and wavelet filters corresponding to the wavelet.

    [LoD,HiD,LoR,HiR] = orthfilt(scalf);

    Confirm the filters form an orthonormal perfect reconstruction wavelet filter bank.

    [tf,checks] = isorthwfb(LoD)
    tf = logical
   1


    checks=7×3 table
                                          Pass-Fail    Maximum Error    Test Tolerance
                                          _________    _____________    ______________

    Equal-length filters                    pass                 0                 0  
    Even-length filters                     pass                 0                 0  
    Unit-norm filters                       pass        1.7665e-10        1.4901e-08  
    Filter sums                             pass        7.2923e-15        1.4901e-08  
    Even and odd downsampled sums           pass        3.7748e-15        1.4901e-08  
    Zero autocorrelation at even lags       pass        7.3088e-11        1.4901e-08  
    Zero crosscorrelation at even lags      pass        1.3089e-17        1.4901e-08

    Create a discrete wavelet transform filter bank using the wavelet. Plot the frequency responses of the wavelet filters and the final resolution scaling filter for the default signal length.

    fb = dwtfilterbank(Wavelet="bl10");
freqz(fb)

    Figure contains an axes object. The axes object with title DWT Filter Bank bl10, xlabel Normalized Frequency (cycles/sample), ylabel Magnitude contains 6 objects of type line. These objects represent D 1, D 2, D 3, D 4, D 5, A 5.

    Plot the wavelet at the coarsest scale.

    [psi,t] = wavelets(fb);
plot(t,psi(end,:))
grid on
title("Wavelet")

    Figure contains an axes object. The axes object with title Wavelet contains an object of type line.

    Plot the scaling function at the coarsest scale.

    [phi,t] = scalingfunctions(fb);
plot(t,phi(end,:))
grid on
title("Scaling Function")

    Figure contains an axes object. The axes object with title Scaling Function contains an object of type line.

    Input Arguments

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    Best-localized Daubechies wavelet, specified as one of these:

    • "bl7" — Best-localized Daubechies wavelet with seven vanishing moments

    • "bl9" — Best-localized Daubechies wavelet with nine vanishing moments

    • "bl10" — Best-localized Daubechies wavelet with 10 vanishing moments

    Output Arguments

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    Scaling filter corresponding to wname, returned as a vector. scalf should be used in conjunction with orthfilt to obtain scaling and wavelet filters with the proper normalization. The scaling filters agree exactly with Doroslovački [1]. The sum of filter coefficients is nearly √2 and the L2 norm is nearly 1.0.

    Data Types: double

    References

    [1] Doroslovački, M.L. “On the Least Asymmetric Wavelets.” IEEE Transactions on Signal Processing 46, no. 4 (April 1998): 1125–30. https://doi.org/10.1109/78.668562.

    Extended Capabilities

    C/C++ Code Generation
    Generate C and C++ code using MATLAB® Coder™.

    Version History

    Introduced in R2022b

    See Also

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