Time-frequency equivalence using chirp signals for frequency response analysis

Time-frequency equivalence using chirp signals for frequency response analysis | 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 Article Time-frequency equivalence using chirp signals for frequency response analysis Resmi Suresh, Raghunathan Rengaswamy This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-134038/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 Frequency response analysis (FRA) of systems is a well-researched area. For years, FRA has been performed using input signals, which are a series of sinusoids or a sum of sinusoids. This results in large experimentation time, particularly when the system has to be probed at lower frequencies. In this work, we describe a previously unknown time-frequency duality for linear systems when probed through chirp signals. We show that the entire frequency response can be extracted with a single chirp signal by extending the notion of instantaneous frequency to both the input and output signals. It is surprising that this powerful result had not been uncovered given that FRA has been used in multiple disciplines for more than hundred years. This result has the possibility of completely revolutionizing methods used for frequency response analysis. Simulation studies that support the main result are described. While this result is of relevance in multiple areas, we demonstrate the potential impact of this result in electrochemical impedance spectroscopy. Physical sciences/Engineering/Chemical engineering Physical sciences/Energy science and technology/Energy modelling Physical sciences/Engineering/Electrical and electronic engineering Physical sciences/Mathematics and computing/Computational science Frequency Response Analysis Nyquist plot Impedance Chirp signals EIS Figures Figure 1 Figure 2 Figure 3 Figure 4 Full Text Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the latest manuscript can be downloaded and accessed as a PDF. Additional Declarations There is NO Competing Interest. 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-134038","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":7620706,"identity":"0ddfe624-6651-4747-9e77-d072aded79ea","order_by":0,"name":"Resmi Suresh","email":"","orcid":"https://orcid.org/0000-0002-7401-5390","institution":"Indian Institute of Technology Guwahati","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Resmi","middleName":"","lastName":"Suresh","suffix":""},{"id":7620707,"identity":"1bcb4d11-f789-478b-a916-4abd25d9e351","order_by":1,"name":"Raghunathan Rengaswamy","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIiWNgGAWjYHACNiC24WGD8niI1ZLGw8ZGopbDEIooYN5+/Npj3j3nZfjkuxMYftQwyJgT0iJzJqfcmOfZbaDDeDcw9hxj4LFsIKBFgiEnTZrnAEQLA28DA4/BAUJa+N+AtJyD2PKXKC0S6ceAWg6AtTATZ4vEGzbJOQeSgVpyNxyWOSZBjMPSn0m8OWBnL998duPDNzU29gS1AOPOAM48AAoOIgD7A2JUjYJRMApGwUgGAGdJM6EPt0RtAAAAAElFTkSuQmCC","orcid":"","institution":"Indian Institute of Technology Madras","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Raghunathan","middleName":"","lastName":"Rengaswamy","suffix":""}],"badges":[],"createdAt":"2020-12-22 12:31:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-134038/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-134038/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":6853719,"identity":"94461af4-d871-4652-b52d-668a192e9c0a","added_by":"auto","created_at":"2021-03-11 19:36:25","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":73176,"visible":true,"origin":"","legend":"Comparison of the working of standard FRA and chirp-based FRA. Standard FRA uses a few\ncycles of multiple sinusoidal signals of di\u000berent frequencies to obtain discrete points in the Nyquist plot.\nChirp-based FRA generates as many points in Nyquist plot as the number of samples in the output signal\nand thus, a smooth and continuous impedance pro\fle is obtained in a short time.","description":"","filename":"f1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-134038/v1/9396d5c2e0f74c7f1b7135c5.jpg"},{"id":6854275,"identity":"03c5fabd-a1f2-41bb-ba23-356a773d8591","added_by":"auto","created_at":"2021-03-11 19:39:26","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":77704,"visible":true,"origin":"","legend":"Response of various systems to linear and fourth order chirp inputs. Zoomed responses are given\nin the inset.","description":"","filename":"f2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-134038/v1/d0ed61a4276def44cfb0b525.jpg"},{"id":6853722,"identity":"425c06e7-079c-4f39-a81a-002304278737","added_by":"auto","created_at":"2021-03-11 19:36:25","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":67262,"visible":true,"origin":"","legend":"Error between actual chirp response (x(t)) and assumed chirp response AinAR( (t)) sin(\u001e(t) +\n\u001eL( (t))) for linear and fourth order chirp responses","description":"","filename":"f3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-134038/v1/17c35ed140bd54795babedbd.jpg"},{"id":6854273,"identity":"bf4df40e-1f56-4d58-818a-c14aeea737be","added_by":"auto","created_at":"2021-03-11 19:39:25","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":70251,"visible":true,"origin":"","legend":"Nyquist plots generated using linear and fourth order chirp analysis in comparison with the\ntheoretical frequency response for various systems. Nyquit plots generated using linear and fourth order\nchirp responses are for the input frequency range [1Hz 400Hz] and [1Hz 1000Hz] respectively.","description":"","filename":"f4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-134038/v1/f8cc5809fd587c352a4e715e.jpg"},{"id":13603268,"identity":"f8f7c68e-46f3-4dd0-b029-51ceb91f29e0","added_by":"auto","created_at":"2021-09-17 05:54:44","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1346072,"visible":true,"origin":"","legend":"","description":"","filename":"NatureComputationalScienceTheoryofChirpAnalysis.pdf","url":"https://assets-eu.researchsquare.com/files/rs-134038/v1_covered.pdf"},{"id":6854403,"identity":"05c425bd-6513-4906-ae5c-0cbb17dbae21","added_by":"auto","created_at":"2021-03-11 19:42:29","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1592495,"visible":true,"origin":"","legend":"","description":"","filename":"NatureComputationalScienceTheoryofChirpAnalysis.pdf","url":"https://assets-eu.researchsquare.com/files/rs-134038/v1_stamped.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Time-frequency equivalence using chirp signals for frequency response analysis","fulltext":[{"header":"Full Text","content":"Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. 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