Quadratic-Phase Scaled Wigner Distribution: Convolution and Correlation

Quadratic-Phase Scaled Wigner Distribution: Convolution and Correlation | 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 Quadratic-Phase Scaled Wigner Distribution: Convolution and Correlation M. Younus Bhat, Aamir H. Dar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2237637/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Jan, 2023 Read the published version in Signal, Image and Video Processing → Version 1 posted 7 You are reading this latest preprint version Abstract In this paper, we propose the novel integral transform coined as the Quadratic-phase Scaled Wigner Distribution (QSWD) by extending the Wigner distri- bution associated with quadratic-phase Fourier trans- form(QWD) to the novel one inspired by the definition of fractional bispectrum. A natural magnification ef- fect characterized by the extra degrees of freedom of the quadratic-phase Fourier transform (QPFT) and by a factor k on the frequency axis enables the QSWD to have flexibility to be used in cross-term reduction. By using the machinery of QSWD and operator theory, we first establish the general properties of the proposed transform, including the conjugate-symmetry, non-linearity, shifting, scaling and marginal. Then, we study the main properties of the proposed transform, including the in- verse, Moyal’s, convolution and correlation. Finally, the applications of the newly defined QSWD for the de- tection of single-component and bi-component linear- frequency-modulated (LFM) signal are also performed to show the advantage of the theory. Mathematics Subject Classification (2020) 42C40 · 81S30 · 11R52 · 44A35. Quadratic-phase Fourier transform Wigner distribution Moyal’s formulae convolution and correlation Linear frequency-modulated signal. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 21 Jan, 2023 Read the published version in Signal, Image and Video Processing → Version 1 posted Editorial decision: Major revision 09 Dec, 2022 Reviews received at journal 23 Nov, 2022 Reviewers agreed at journal 13 Nov, 2022 Reviewers invited by journal 12 Nov, 2022 Editor assigned by journal 12 Nov, 2022 Submission checks completed at journal 04 Nov, 2022 First submitted to journal 04 Nov, 2022 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-2237637","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":149546941,"identity":"ad9d3d25-f30a-427d-a5ba-ee05ee5e44f6","order_by":0,"name":"M. 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