Algebraic Foundations of Generalized Signal Processing: A Unified Approach Across Domains

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Notice

nThis is an unedited manuscript accepted for publication and provided as an Article in Press for early access at the author’s request. The article will undergo copyediting, typesetting, and galley proof review before final publication. Please be aware that errors may be identified during production that could affect the content. All legal disclaimers of the journal apply.n

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Year : 2025 [if 2224 equals=””]29/09/2025 at 4:59 PM[/if 2224] | [if 1553 equals=””] Volume : 15 [else] Volume : 15[/if 1553] | [if 424 equals=”Regular Issue”]Issue : [/if 424][if 424 equals=”Special Issue”]Special Issue[/if 424] [if 424 equals=”Conference”][/if 424] 03 | Page : 33 44

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    By

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    V. Basil Hans,

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  1. Professor, Department of Management & Commerce, Srinivas University in Mangalore, Karnataka, India

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Abstract

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nUsing the techniques of algebra, notably polynomial algebras and modules, algebraic signal processing (ASP) is a contemporary, abstract framework that generalizes conventional signal processing— including Fourier analysis, filtering, and convolution. The notion is to use algebraic structures to explain signals, systems, and transformations such that ideas may be understood and generalized across many domains, including time, space, graph, or group. A unifying theoretical framework called ASP generalizes classical signal processing utilizing algebraic structures, especially polynomial algebras and modules. ASP models signal as module elements over a selected algebra; filters are shown as algebra elements operating on the signal space. A systematic approach to signal operations like shifting, filtering, and spectral analysis in a wide spectrum of domains—including time, space, and graphs—is made possible by this abstract concept. By use of module decomposition and representation theory, the framework offers a profound understanding of the design of Fourier-like transforms, therefore enabling innovative ideas in areas including graph signal processing, image analysis, and multidimensional data representation. ASP not only generalizes classical methods but also helps to create novel transforms suited to uneven or non-Euclidean structures by capturing the core of signal processing in algebraic terms.nn

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Keywords: Graph signal processing, spectral analysis, Fourier transform, signal modules, polynomial algebras

n[if 424 equals=”Regular Issue”][This article belongs to Current Trends in Signal Processing ]

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How to cite this article:
nV. Basil Hans. [if 2584 equals=”][226 wpautop=0 striphtml=1][else]Algebraic Foundations of Generalized Signal Processing: A Unified Approach Across Domains[/if 2584]. Current Trends in Signal Processing. 26/09/2025; 15(03):33-44.

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nV. Basil Hans. [if 2584 equals=”][226 striphtml=1][else]Algebraic Foundations of Generalized Signal Processing: A Unified Approach Across Domains[/if 2584]. Current Trends in Signal Processing. 26/09/2025; 15(03):33-44. Available from: https://journals.stmjournals.com/ctsp/article=26/09/2025/view=0

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[if 424 not_equal=””]Regular Issue[else]Published[/if 424] Subscription Review Article

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Current Trends in Signal Processing

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[if 344 not_equal=””]ISSN: 2277–6176[/if 344]

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Volume 15
[if 424 equals=”Regular Issue”]Issue[/if 424][if 424 equals=”Special Issue”]Special Issue[/if 424] [if 424 equals=”Conference”][/if 424] 03
Received 10/05/2025
Accepted 24/06/2025
Published 26/09/2025
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Publication Time 139 Days

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