fbspwavf

Complex frequency B-spline wavelet

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    Syntax

    [psi,x] = fbspwavf(lb,ub,n,m,fb,fc)

    Description

    [psi,x] = fbspwavf(lb,ub,n,m,fb,fc) returns values psi of the complex frequency B-spline wavelet defined by the order parameter m, bandwidth parameter fb, and wavelet center frequency fc. The wavelet is evaluated on the n-point regular grid x in the interval [lb,ub]. The general expression for the wavelet is

    ψ(x)=fb sincm(fb x/m) exp(2πi fc x),

    where

    sinct={sinπtπtt≠0,1t=0.

    example

    Examples

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    Open Live Script

    Specify the order, bandwidth, and center frequency parameters of the complex frequency B-spline wavelet fbsp2-0.5-1.

    m = 2;
fb = 0.5;
fc = 1;

    Specify the closed interval [-20,20]. 

    lb = -20;
ub = 20;

    Evaluate the fbsp2-0.5-1 wavelet on a 1000-point regular grid in the closed interval.

    n = 1000;
[psi,x] = fbspwavf(lb,ub,n,m,fb,fc);

    Plot the real and imaginary parts of the wavelet.

    tiledlayout(2,1)
nexttile
plot(x,real(psi))
title({"Complex Frequency B-Spline Wavelet fbsp2-0.5-1","Real Part"})
grid on
nexttile
plot(x,imag(psi))
title("Imaginary Part")
grid on

    Figure contains 2 axes objects. Axes object 1 with title Complex Frequency B-Spline Wavelet fbsp2-0.5-1 Real Part contains an object of type line. Axes object 2 with title Imaginary Part contains an object of type line.

    Input Arguments

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    Closed interval [lb,ub], specified by the scalars lb and ub, where lb < ub.

    Data Types: double

    Number of regularly spaced points in the interval [lb,ub], specified as a positive integer. The wavelet is evaluated at these points.

    Data Types: double

    Order parameter of the wavelet, specified as a positive integer m ≥ 1.

    Data Types: double

    Wavelet frequency parameters, specified by the positive scalars fb > 0 and fc > 0. fb is the bandwidth, and fc is the center frequency.

    Data Types: double

    Output Arguments

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    Complex frequency B-spline wavelet evaluated on the n-point regular grid [lb,ub], returned as a complex-valued vector.

    Grid points where the complex frequency B-spline wavelet is evaluated, returned as a 1-by-n vector. The points are evenly distributed in the interval [lb,ub].

    References

    [1] Teolis, Anthony. Computational Signal Processing with Wavelets. Boston, MA: Birkhäuser Boston, 1998. https://doi.org/10.1007/978-1-4612-4142-3.

    Version History

    Introduced before R2006a

    See Also