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shanwavf

Complex Shannon wavelet

    Description

    example

    [psi,x] = shanwavf(lb,ub,n,fb,fc) returns values psi of the complex Shannon wavelet evaluated on the n point regular grid in the interval [lb,ub]. The wavelet is defined by a bandwidth parameter fb and center frequency fc.

    Examples

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    Obtain and plot a complex Shannon wavelet. Set the bandwidth and center frequency parameters.

    fb = 1;
    fc = 1.5;

    Set the effective support and number of sample points.

    lb = -10; 
    ub = 10; 
    n = 1000;

    Obtain the complex-valued Shannon wavelet and plot the real and imaginary parts.

    [psi,x] = shanwavf(lb,ub,n,fb,fc);
    tiledlayout(2,1)
    nexttile
    plot(x,real(psi))
    title("Complex Shannon Wavelet")
    xlabel("Real Part")
    grid on
    nexttile
    plot(x,imag(psi))
    xlabel("Imaginary Part")
    grid on

    Input Arguments

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    Interval endpoints lbub, specified as a pair of real-valued scalars.

    Data Types: double

    Number of regularly spaced points in the interval [lb,ub], specified as a positive integer.

    Data Types: double

    Bandwidth parameter of the complex Shannon wavelet, specified as a positive scalar.

    Data Types: double

    Center frequency of the complex Shannon wavelet, specified as a positive scalar.

    Data Types: double

    Output Arguments

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    Complex Shannon wavelet evaluated on the n point regular grid x in the interval [lb,ub], returned as a 1-by-n vector.

    Grid where the complex Shannon wavelet is evaluated, returned as a 1-by-n vector. The sample points are evenly distributed between lb and ub.

    More About

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    Complex Shannon Wavelet

    The complex Shannon wavelet is defined as

    ψ(x)=fbsinc(fbx)exp(2πifcx),

    where fb is the bandwidth parameter and fc is the center frequency.

    References

    [1] Teolis, Anthony. Computational Signal Processing with Wavelets. Modern Birkhäuser Classics. Cham: Springer International Publishing, 2017. https://doi.org/10.1007/978-3-319-65747-9.

    Version History

    Introduced before R2006a

    See Also