A Novel Direct Calculation Algorithm using Taylor Expansion in FPGA for DDS Signal Quality Enhancement

A Novel Direct Calculation Algorithm using Taylor Expansion in FPGA for DDS Signal Quality Enhancement | 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 Novel Direct Calculation Algorithm using Taylor Expansion in FPGA for DDS Signal Quality Enhancement Dingyi Ma, Ze Liu, Jingming Cao, Junjie Li, Zewen Wan, Yizhou Zhou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6712642/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 30 Sep, 2025 Read the published version in Analog Integrated Circuits and Signal Processing → Version 1 posted 11 You are reading this latest preprint version Abstract The precision measurement of capacitance necessitates the utilisation of a precision capacitance bridge, wherein a sine signal serves as a reference. Consequently, the precision of the sine signal is of paramount importance for the precision measurement of capacitance. In the conventional method of generating a sine signal , a look-up table is employed as the data source. However, the look-up table approach necessitates an excessive amount of read-only memory space to fulfil the requirements of high-precision scenarios. In this paper, we proposes an novel algorithm based on Taylor expansion to calculate the sine function. This algorithm doesn’t use any read-only storage space. Compared with the Coordinate Rotation Digital Computer algorithm in computer, it is based on the pipelined architecture to balance latency and digital signal processor resource consumption. For the Lagrange residual term error problem of Taylor expansion, the optimization algorithm using trigonometric periodicity and the complementary algorithm of sine and cosine functions is proposed. To evaluate the accuracy of the sine function generated by the algorithm, direct digital synthesis and digital to analog converter outputs are utilized to improve the accuracy and enhance the total harmonic distortion as compared to the conventional algorithm. Direct Digital Synthesizer Taylor Expansion sine wave harmonic analysis signal-to-noise ratio Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 30 Sep, 2025 Read the published version in Analog Integrated Circuits and Signal Processing → Version 1 posted Editorial decision: Revision requested 19 Jun, 2025 Reviews received at journal 19 Jun, 2025 Reviews received at journal 13 Jun, 2025 Reviewers agreed at journal 29 May, 2025 Reviews received at journal 26 May, 2025 Reviewers agreed at journal 26 May, 2025 Reviewers agreed at journal 23 May, 2025 Reviewers invited by journal 23 May, 2025 Editor assigned by journal 21 May, 2025 Submission checks completed at journal 21 May, 2025 First submitted to journal 21 May, 2025 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-6712642","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":461031393,"identity":"9a0da66b-b2a2-43f3-9c9d-34c3deecc080","order_by":0,"name":"Dingyi Ma","email":"","orcid":"","institution":"Beijing Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Dingyi","middleName":"","lastName":"Ma","suffix":""},{"id":461031394,"identity":"ca888a49-8abf-49e5-826e-6dbe6fc6c54a","order_by":1,"name":"Ze Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAu0lEQVRIiWNgGAWjYDACdsYGho8NbGC2BHFamBkbGGc2sEmQogWIeBsYSNAi38zcJm27g6/O4ADzwds8DHZ5BLUwNjO2SeeeYZMwOMCWbM3DkFxM2F3MIC1tIC08ZtI8DAcSGwhpYQNpsQRr4f9GnBYekBZGiC1sxGmRYGZstuw9wyY58zCbseUcg2TCWuTb2x/e+LnjGD/f8eaHN95U2BHWAgXHwBHEwGBApHogqCFe6SgYBaNgFIw8AABRXDBrlzAdSwAAAABJRU5ErkJggg==","orcid":"","institution":"Beijing Jiaotong University","correspondingAuthor":true,"prefix":"","firstName":"Ze","middleName":"","lastName":"Liu","suffix":""},{"id":461031395,"identity":"76ea7b5e-fdf6-4f17-a711-e8b6bb8078f4","order_by":2,"name":"Jingming Cao","email":"","orcid":"","institution":"Beijing Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Jingming","middleName":"","lastName":"Cao","suffix":""},{"id":461031398,"identity":"34f8e326-dc68-47be-8ce4-7b61eccc85ec","order_by":3,"name":"Junjie Li","email":"","orcid":"","institution":"Beijing Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Junjie","middleName":"","lastName":"Li","suffix":""},{"id":461031399,"identity":"0ecc4361-e639-4495-87fa-ae10aee7e316","order_by":4,"name":"Zewen Wan","email":"","orcid":"","institution":"Beijing Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Zewen","middleName":"","lastName":"Wan","suffix":""},{"id":461031400,"identity":"876ed9b4-8e10-407b-897f-66f631a98fbb","order_by":5,"name":"Yizhou Zhou","email":"","orcid":"","institution":"Beijing Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Yizhou","middleName":"","lastName":"Zhou","suffix":""}],"badges":[],"createdAt":"2025-05-21 05:23:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6712642/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6712642/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10470-025-02473-2","type":"published","date":"2025-09-30T15:58:12+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":92883890,"identity":"9f42e9fd-b2c5-420c-9395-d7cab843af3d","added_by":"auto","created_at":"2025-10-06 16:10:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1488980,"visible":true,"origin":"","legend":"","description":"","filename":"snarticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6712642/v1_covered_b03658ab-ada2-4b17-ac66-ea2e996cfc23.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Novel Direct Calculation Algorithm using Taylor Expansion in FPGA for DDS Signal Quality Enhancement","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"analog-integrated-circuits-and-signal-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"alog","sideBox":"Learn more about [Analog Integrated Circuits and Signal Processing](http://link.springer.com/journal/10470)","snPcode":"10470","submissionUrl":"https://submission.nature.com/new-submission/10470/3","title":"Analog Integrated Circuits and Signal Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Direct Digital Synthesizer, Taylor Expansion, sine wave, harmonic analysis, signal-to-noise ratio","lastPublishedDoi":"10.21203/rs.3.rs-6712642/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6712642/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The precision measurement of capacitance necessitates the utilisation of a precision capacitance bridge, wherein a sine signal serves as a reference. Consequently, the precision of the sine signal is of paramount importance for the precision measurement of capacitance. In the conventional method of generating a sine signal , a look-up table is employed as the data source. However, the look-up table approach necessitates an excessive amount of read-only memory space to fulfil the requirements of high-precision scenarios. In this paper, we proposes an novel algorithm based on Taylor expansion to calculate the sine function. This algorithm doesn’t use any read-only storage space. Compared with the Coordinate Rotation Digital Computer algorithm in computer, it is based on the pipelined architecture to balance latency and digital signal processor resource consumption. For the Lagrange residual term error problem of Taylor expansion, the optimization algorithm using trigonometric periodicity and the complementary algorithm of sine and cosine functions is proposed. To evaluate the accuracy of the sine function generated by the algorithm, direct digital synthesis and digital to analog converter outputs are utilized to improve the accuracy and enhance the total harmonic distortion as compared to the conventional algorithm.","manuscriptTitle":"A Novel Direct Calculation Algorithm using Taylor Expansion in FPGA for DDS Signal Quality Enhancement","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-26 07:18:06","doi":"10.21203/rs.3.rs-6712642/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-06-19T10:38:09+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-19T10:33:34+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-13T21:10:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"247547788850573037278411932756118524267","date":"2025-05-29T19:14:32+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-26T12:54:36+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"313925825208517339000836759951416351111","date":"2025-05-26T12:09:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"191820037878388232607146721542912065878","date":"2025-05-23T09:39:06+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-05-23T09:12:01+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-05-21T12:42:32+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-05-21T12:41:57+00:00","index":"","fulltext":""},{"type":"submitted","content":"Analog Integrated Circuits and Signal Processing","date":"2025-05-21T05:10:29+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"analog-integrated-circuits-and-signal-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"alog","sideBox":"Learn more about [Analog Integrated Circuits and Signal Processing](http://link.springer.com/journal/10470)","snPcode":"10470","submissionUrl":"https://submission.nature.com/new-submission/10470/3","title":"Analog Integrated Circuits and Signal Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"7c8bdc98-2afd-434f-a8fc-63529e5e8d3d","owner":[],"postedDate":"May 26th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-10-06T16:04:40+00:00","versionOfRecord":{"articleIdentity":"rs-6712642","link":"https://doi.org/10.1007/s10470-025-02473-2","journal":{"identity":"analog-integrated-circuits-and-signal-processing","isVorOnly":false,"title":"Analog Integrated Circuits and Signal Processing"},"publishedOn":"2025-09-30 15:58:12","publishedOnDateReadable":"September 30th, 2025"},"versionCreatedAt":"2025-05-26 07:18:06","video":"","vorDoi":"10.1007/s10470-025-02473-2","vorDoiUrl":"https://doi.org/10.1007/s10470-025-02473-2","workflowStages":[]},"version":"v1","identity":"rs-6712642","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6712642","identity":"rs-6712642","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}