{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T06:47:03Z","timestamp":1781246823985,"version":"3.54.1"},"reference-count":43,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T00:00:00Z","timestamp":1713225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42204116"],"award-info":[{"award-number":["42204116"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271428"],"award-info":[{"award-number":["12271428"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2020YFA0713403"],"award-info":[{"award-number":["2020YFA0713403"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key Research and Development Program of China","award":["42204116"],"award-info":[{"award-number":["42204116"]}]},{"name":"National Key Research and Development Program of China","award":["12271428"],"award-info":[{"award-number":["12271428"]}]},{"name":"National Key Research and Development Program of China","award":["2020YFA0713403"],"award-info":[{"award-number":["2020YFA0713403"]}]},{"name":"Opening Project of Guangxi Wireless Broadband Communication and Signal Processing Key Laboratory","award":["42204116"],"award-info":[{"award-number":["42204116"]}]},{"name":"Opening Project of Guangxi Wireless Broadband Communication and Signal Processing Key Laboratory","award":["12271428"],"award-info":[{"award-number":["12271428"]}]},{"name":"Opening Project of Guangxi Wireless Broadband Communication and Signal Processing Key Laboratory","award":["2020YFA0713403"],"award-info":[{"award-number":["2020YFA0713403"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The instantaneous frequency (IF) is an important feature for the analysis of nonstationary signals. For IF estimation, the time\u2013frequency representation (TFR)-based algorithm is used in a common class of methods. TFR-based methods always need the representation concentrated around the \u201ctrue\u201d IFs and the number of components within the signal. In this paper, we propose a novel method to adaptively estimate the IFs of nonstationary signals, even for weak components of the signals. The proposed technique is not based on the TFR: it is based on the frequency estimation operator (FEO), and the short-time Fourier transform (STFT) is used as its basis. As we know, the FRO is an exact estimation of the IF for weak frequency-modulated (FM) signals, but is not appropriate for strong FM modes. Through theoretical derivation, we determine that the fixed points of the FEOwith respect to the frequency are equivalent to the ridge of the STFT spectrum. Furthermore, the IF of the linear chirp signals is just the fixed points of the FEO. Therefore, we apply the fixed-point algorithm to the FEO to realize the precise and reliable estimation of the IF, even for highly FM signals. Finally, the results using synthetic and real signals show the utility of the proposed method for IF estimation and that it is more robust than the compared method. It should be noted that the proposed method employing the FEO only computes the first-order differential of the STFT for the chirp-like signals, while it can provide a result derived using the second-order estimation operator. Moreover, this new method is effective for the IF estimation of weak components within a signal.<\/jats:p>","DOI":"10.3390\/rs16081412","type":"journal-article","created":{"date-parts":[[2024,4,17]],"date-time":"2024-04-17T07:54:36Z","timestamp":1713340476000},"page":"1412","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Instantaneous Frequency Extraction for Nonstationary Signals via a Squeezing Operator with a Fixed-Point Iteration Method"],"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":[{"vocabulary":"crossref","role":"author"}]},{"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":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fengyuan","family":"Sun","sequence":"additional","affiliation":[{"name":"Guangxi Wireless Broadband Communication and Signal Processing Key Laboratory, The School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Zhang","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":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,16]]},"reference":[{"key":"ref_1","first-page":"510","article-title":"Estimating and interpreting the instantaneous frequency of a signal. 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