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Polarization-multiplexed nonlinear inverse synthesis with standard and reduced-complexity NFT processing: erratum.

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    This study corrects a formula for the numerical nonlinear Fourier transform. The core findings and conclusions remain consistent with the original work.

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    Area of Science:

    • Mathematics
    • Signal Processing
    • Applied Physics

    Background:

    • The numerical nonlinear Fourier transform is a critical tool in analyzing complex data.
    • Accurate formulas are essential for reliable transform application.

    Purpose of the Study:

    • To identify and rectify an error in a previously published formula for the numerical nonlinear Fourier transform.
    • To ensure the continued accuracy and reliability of this mathematical tool.

    Main Methods:

    • Detailed mathematical analysis of the existing formula.
    • Derivation of the corrected formula through rigorous theoretical work.

    Main Results:

    • A specific formula for the numerical nonlinear Fourier transform has been corrected.
    • The correction ensures greater precision in numerical computations.

    Conclusions:

    • The corrected formula maintains the integrity of the numerical nonlinear Fourier transform.
    • The fundamental conclusions derived using this transform remain valid and unchanged.