{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T04:52:37Z","timestamp":1768452757196,"version":"3.49.0"},"reference-count":35,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2023,9,25]],"date-time":"2023-09-25T00:00:00Z","timestamp":1695600000000},"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":["61761027"],"award-info":[{"award-number":["61761027"]}],"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":["22JR5RA381"],"award-info":[{"award-number":["22JR5RA381"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Gansu Youth Science and Technology Fund Project","award":["61761027"],"award-info":[{"award-number":["61761027"]}]},{"name":"Gansu Youth Science and Technology Fund Project","award":["22JR5RA381"],"award-info":[{"award-number":["22JR5RA381"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>At present, the micro-Doppler effects of underwater targets is a challenging new research problem. This paper studies the micro-Doppler effect of underwater targets, analyzes the moving characteristics of underwater micro-motion components, establishes echo models of harmonic vibration points and plane and rotating propellers, and reveals the complex modulation laws of the micro-Doppler effect. In addition, since an echo is a multi-component signal superposed by multiple modulated signals, this paper provides a sparse reconstruction method combined with time\u2013frequency distributions and realizes signal separation and time\u2013frequency analysis. A MicroDopplerlet time\u2013frequency atomic dictionary, matching the complex modulated form of echoes, is designed, which effectively realizes the concise representation of echoes and a micro-Doppler effect analysis. Meanwhile, the needed micro-motion parameter information for underwater signal detection and recognition is extracted.<\/jats:p>","DOI":"10.3390\/s23198066","type":"journal-article","created":{"date-parts":[[2023,9,25]],"date-time":"2023-09-25T04:15:38Z","timestamp":1695615338000},"page":"8066","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Micro-Doppler Effect and Sparse Representation Analysis of Underwater Targets"],"prefix":"10.3390","volume":"23","author":[{"given":"Yan","family":"Lu","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}]},{"given":"Siwei","family":"Kou","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"given":"Xiaopeng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,25]]},"reference":[{"key":"ref_1","unstructured":"Chen, V.C. 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