A Fast and Accurate Method for Numerical Integration of Bandwidth-Limited Signals

A Fast and Accurate Method for Numerical Integration of Bandwidth-Limited Signals | 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 A Fast and Accurate Method for Numerical Integration of Bandwidth-Limited Signals Mary S. Wei This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7801844/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 Fast and accurate integration of images or signals is important in many applications. This paper reports a novel split-band integrator (SBI) that is especially suitable for integrating discrete images representing a bandwidth-limited signal sampled above its Nyquist frequency. The SBI combines the advantages of the classical Newton-Cotes formulas (NCFs) and a fast Fourier transform (FFT) based integrator while avoiding their drawbacks. It works by splitting an input into two images and processing them separately then combining the results, where one image containing high-frequency components is integrated using FFT, whereas the other collecting the remaining low-frequency portion is integrated accurately by a classical NCF. Both theoretical derivations and numerical tests are presented to demonstrate the SBI. Electrical Engineering Numerical integration Nyquist-Shannon sampling Newton-Cotes formulas fast Fourier transform Full Text Additional Declarations The authors declare no competing interests. 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. 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