csymwavf

Complex symlet wavelet filter

Since R2026a

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    Syntax

    f = csymwavf(wname)

    Description

    f = csymwavf(wname) returns the scaling filter associated with the complex-valued least asymmetric Daubechies wavelet (complex symlet) specified by wname.

    To learn which functions support complex symlets, see Discrete Wavelet Transform Functions and Complex Symlets.

    example

    Examples

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    This example uses:

    Open Live Script

    Obtain the scaling filter associated with the complex symlet with four vanishing moments.

    n = 4;
scf = csymwavf("csym"+num2str(n));

    Confirm that the filter coefficients are normalized such that their sum is equal to 1.

    sum(scf)
    ans = 
1.0000 + 0.0000i

    Plot the real and imaginary parts of the filter coefficients. Because the symlet has an even number of vanishing moments, the filter coefficients are not symmetric about the midpoint.

    stem(real(scf),"o-")
hold on
stem(imag(scf),"x-")
hold off
grid on
legend("Real","Imaginary")
title("Scaling Filter Coefficients: "+num2str(n)+" Vanishing Moments")

    Figure contains an axes object. The axes object with title Scaling Filter Coefficients: 4 Vanishing Moments contains 2 objects of type stem. These objects represent Real, Imaginary.

    Use the function phasez (Signal Processing Toolbox) to plot the phase response. Because the complex symlet is an orthogonal wavelet with compact support, the filter response deviates noticeably from linear phase.

    [phz,w] = phasez(scf);

plot(w/pi,phz)
hold on
plot([w(1)/pi w(end)/pi], [phz(1) phz(end)])
grid on
hold off
axis tight
legend("Filter Phase","Linear Phase")
title("Phase Response: "+num2str(n)+" Vanishing Moments")
xlabel("Normalized Frequency ($\times\pi$ rad/sample)", ...
    "Interpreter","latex")

    Figure contains an axes object. The axes object with title Phase Response: 4 Vanishing Moments, xlabel Normalized Frequency ($ times pi $ rad/sample) contains 2 objects of type line. These objects represent Filter Phase, Linear Phase.

    Obtain the scaling filter associated with the complex symlet with five vanishing moments.

    n = 5;
scf = csymwavf("csym"+num2str(n));

    Confirm the filter coefficients are normalized such that their sum is equal to 1.

    sum(scf)
    ans = 
1.0000 - 0.0000i

    Plot the real and imaginary parts of the filter coefficients. Because the symlet has an odd number of vanishing moments, the filter coefficients are symmetric about the midpoint.

    stem(real(scf),"o-")
hold on
stem(imag(scf),"x-")
hold off
grid on
legend("Real","Imaginary")
title("Scaling Filter Coefficients: "+num2str(n)+" Vanishing Moments")

    Figure contains an axes object. The axes object with title Scaling Filter Coefficients: 5 Vanishing Moments contains 2 objects of type stem. These objects represent Real, Imaginary.

    Plot the phase response. With an odd number of vanishing moments, you can get almost linear phase.

    [phz,w] = phasez(scf);

plot(w/pi,phz)
hold on
plot([w(1)/pi w(end)/pi], [phz(1) phz(end)])
grid on
hold off
axis tight
legend("Filter Phase","Linear Phase")
title("Phase Response: "+num2str(n)+" Vanishing Moments")
xlabel("Normalized Frequency ($\times\pi$ rad/sample)", ...
    "Interpreter","latex")

    Figure contains an axes object. The axes object with title Phase Response: 5 Vanishing Moments, xlabel Normalized Frequency ($ times pi $ rad/sample) contains 2 objects of type line. These objects represent Filter Phase, Linear Phase.

    Input Arguments

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    Complex symlet with N vanishing moments, where N is a positive integer between 3 and 45 inclusive.

    Output Arguments

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    Scaling filter associated with the complex symlet wname, returned as a complex-valued vector. The filter is normalized such that the sum of the coefficients equals 1.

    More About

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    References

    [1] Daubechies, Ingrid. “Orthonormal Bases of Compactly Supported Wavelets.” Communications on Pure and Applied Mathematics 41, no. 7 (1988): 909–96. https://doi.org/10.1002/cpa.3160410705.

    [2] Lawton, W. “Applications of Complex Valued Wavelet Transforms to Subband Decomposition.” IEEE Transactions on Signal Processing 41, no. 12 (1993): 3566–68. https://doi.org/10.1109/78.258098.

    [3] Lina, Jean-Marc, and Michel Mayrand. “Complex Daubechies Wavelets.” Applied and Computational Harmonic Analysis 2, no. 3 (1995): 219–29. https://doi.org/10.1006/acha.1995.1015.

    [4] Xiao-Ping Zhang, M.D. Desai, and Ying-Ning Peng. “Orthogonal Complex Filter Banks and Wavelets: Some Properties and Design.” IEEE Transactions on Signal Processing 47, no. 4 (1999): 1039–48. https://doi.org/10.1109/78.752601.

    Extended Capabilities

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

    GPU Code Generation
    Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

    Version History

    Introduced in R2026a

    See Also

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