Fourier Analysis of Signals on Directed Acyclic Graphs (DAG) Using Graph Zero-Padding

Fourier Analysis of Signals on Directed Acyclic Graphs (DAG) Using Graph Zero-Padding | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Fourier Analysis of Signals on Directed Acyclic Graphs (DAG) Using Graph Zero-Padding Ljubisa Stankovic, Miloš Daković, Ali Bagheri Bardi, Miloš Brajović, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4360629/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Directed acyclic graphs (DAGs) are used for modeling causal relationships, dependencies, and flows in various systems. However, spectral analysis becomes impractical in this setting because the eigendecomposition of the adjacency matrix yields all eigenvalues equal to zero. This inherent property of DAGs results in an inability to differentiate between frequency components of signals on such graphs. This problem can be addressed by alternating the Fourier basis or adding edges in a DAG. However, these approaches change the physics of the considered problem. To address this limitation, we propose a graph zero-padding approach. This approach involves augmenting the original DAG with additional vertices that are connected to the existing structure. The added vertices are characterized by signal values set to zero. The proposed technique enables the spectral evaluation of system outputs on DAGs (in almost all cases), that is the computation of vertex-domain convolution without the adverse effects of aliasing due to changes in a graph structure, with the ultimate goal of preserving the output of the system on a graph as if the changes in the graph structure were not performed. Directed Acycle Graph Graph Signal Processing Graph Fourier Transform Zero Padding Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4360629","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":298208406,"identity":"e2041e5d-e3aa-497d-a210-2c2021cec4b1","order_by":0,"name":"Ljubisa Stankovic","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAy0lEQVRIiWNgGAWjYBACPoYDbAwJDAxyxGthg2oxJkULCDEwJDYQr4XxjNmDB3/s0jccP36B4UcNQzQ/YVvOmBsktiXnbjiTU8DYc4whdyYh+4BazCQSG5hzN9zgSWDgbWDI3XCAGC0Jf+rTDYBaGP8CtewnTgvb4QSDG+wHmMG2EPbLsXKgX44bzjyTw3BY5phE7gxCtvBLHN728Mefanm+48cfPnxTY5Pb30DIGgm4oTwGQKYEIfUga+CGsj8gQvkoGAWjYBSMRAAAMZZB3s8IgQ4AAAAASUVORK5CYII=","orcid":"","institution":"University of Montenegro","correspondingAuthor":true,"prefix":"","firstName":"Ljubisa","middleName":"","lastName":"Stankovic","suffix":""},{"id":298208409,"identity":"7ea770b4-b750-4f49-82d7-e283ffd005ca","order_by":1,"name":"Miloš Daković","email":"","orcid":"","institution":"University of Montenegro","correspondingAuthor":false,"prefix":"","firstName":"Miloš","middleName":"","lastName":"Daković","suffix":""},{"id":298208412,"identity":"bf94b72f-9112-48ee-add1-aa0e0a09b5ac","order_by":2,"name":"Ali Bagheri Bardi","email":"","orcid":"","institution":"Persian Gulf University","correspondingAuthor":false,"prefix":"","firstName":"Ali","middleName":"Bagheri","lastName":"Bardi","suffix":""},{"id":298208421,"identity":"2ad774bf-9466-4f3d-8bab-9f3d3089edae","order_by":3,"name":"Miloš Brajović","email":"","orcid":"","institution":"University of Montenegro","correspondingAuthor":false,"prefix":"","firstName":"Miloš","middleName":"","lastName":"Brajović","suffix":""},{"id":298208425,"identity":"f5bccd15-1092-4f6e-9c2b-7d66d0782cf8","order_by":4,"name":"Isidora Stanković","email":"","orcid":"","institution":"University of Montenegro","correspondingAuthor":false,"prefix":"","firstName":"Isidora","middleName":"","lastName":"Stanković","suffix":""}],"badges":[],"createdAt":"2024-05-02 18:26:49","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4360629/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4360629/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":82577943,"identity":"491cbc80-b4cb-4788-b124-80310b77b226","added_by":"auto","created_at":"2025-05-13 06:03:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":738238,"visible":true,"origin":"","legend":"","description":"","filename":"GZPJBD.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4360629/v1_covered_6efcdb65-6b58-4bce-82e1-97d7cbd37dfa.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Fourier Analysis of Signals on Directed Acyclic Graphs (DAG) Using Graph Zero-Padding","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Directed Acycle Graph, Graph Signal Processing, Graph Fourier Transform, Zero Padding","lastPublishedDoi":"10.21203/rs.3.rs-4360629/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4360629/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Directed acyclic graphs (DAGs) are used for modeling causal relationships, dependencies, and flows in various systems. 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