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In this paper, based on the novel short-time fractional Fourier transform (STFRFT), a new modified STFRFT is first proposed which can also generalize the properties of the modified short-time Fourier transform (STFT). Then, in the modified STFRFT domain, we derive the instantaneous frequency estimator for the chirp signal and present a new type of synchrosqueezing STFRFT (FRSST). The proposed FRSST presents many results similar to those of the synchrosqueezing STFT (FSST), and it extends the harmonic signal to a chirp signal that offers attractive new features. Furthermore, we provide a detailed analysis of the signal reconstruction, theories, and some properties of the proposed FRSST. Several experiments are conducted, and all of the results illustrate that the proposed FRSST is more effective than the FSST. Finally, based on the linear amplitude modulation and frequency modulation signal, we present a derivation for analyzing the limitations of the FRSST.<\/jats:p>","DOI":"10.3390\/rs16071173","type":"journal-article","created":{"date-parts":[[2024,3,27]],"date-time":"2024-03-27T12:41:57Z","timestamp":1711543317000},"page":"1173","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["The Synchrosqueezed Method and Its Theory-Analysis-Based Novel Short-Time Fractional Fourier Transform for Chirp Signals"],"prefix":"10.3390","volume":"16","author":[{"given":"Zhen","family":"Li","sequence":"first","affiliation":[{"name":"The National Engineering Research Center for Offshore Oil and Gas Exploration, School of Information and Communications Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaoqi","family":"Gao","sequence":"additional","affiliation":[{"name":"The National Engineering Research Center for Offshore Oil and Gas Exploration, School of Information and Communications Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3750-1071","authenticated-orcid":false,"given":"Liang","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jiujiang University, Jiujiang 332005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinghuai","family":"Gao","sequence":"additional","affiliation":[{"name":"The National Engineering Research Center for Offshore Oil and Gas Exploration, School of Information and Communications Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zongben","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,27]]},"reference":[{"key":"ref_1","unstructured":"Bracewell, R. 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