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The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
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The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
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In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
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The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is a crucial tool in the analysis of discrete-time systems, but its convergence is limited to specific values of the complex variable z. This range of values, known as the Region of Convergence (ROC), is fundamental in determining the behavior and stability of a system or signal. The ROC defines the region in the complex plane where the z-transform converges, which can take various...
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Updated: Sep 12, 2025

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Correction: Bessel statistical convergence: New concepts and applications in sequence theory.

Ibrahim S Ibrahim, Majeed A Yousif, Pshtiwan Othman Mohammed

    Plos One
    |August 5, 2025
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    Summary

    This study corrects a previously published article DOI. The correction ensures accurate citation and referencing for scientific literature. Researchers should use the updated information for all future citations.

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    Area of Science:

    • Scientific Publishing
    • Scholarly Communication
    • Bibliometrics

    Context:

    • Correction of a published article's Digital Object Identifier (DOI).
    • Ensuring accuracy in academic referencing and citation practices.
    • Maintaining the integrity of the scientific record.

    Purpose:

    • To provide the correct DOI for the article originally published as 10.1371/journal.pone.0313273.
    • To facilitate accurate retrieval and citation of the research.
    • To uphold standards of scholarly communication.

    Summary:

    • The article DOI has been corrected to ensure proper attribution.
    • This correction is essential for researchers citing the work.
    • Accurate DOIs are critical for the discoverability of scientific publications.

    Impact:

    • Improved accuracy in scientific literature databases.
    • Enhanced reliability of citation tracking and impact analysis.
    • Facilitation of seamless access to the corrected research article.