{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:29:18Z","timestamp":1760232558790,"version":"build-2065373602"},"reference-count":57,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2022,11,17]],"date-time":"2022-11-17T00:00:00Z","timestamp":1668643200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["20-05-00189 A"],"award-info":[{"award-number":["20-05-00189 A"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The concept of the phase space plays a key role in the analysis of oscillating signals. For a 1-D signal, the coordinates of the 2-D phase space are the observation time and the instant frequency. For measurements of propagating wave fields, the time and instant frequency are linked to the spatial location and wave normal, defining a ray. In this case, the phase space is also termed the ray space. Distributions in the ray space find important applications in the analysis of radio occultation (RO) data because they allow the separation of interfering rays in multipath zones. Examples of such distributions are the spectrogram, Wigner distribution function (WDF), and Kirkwood distribution function (KDF). In this study, we analyze the application of the fractional Fourier transform (FrFT) to the construction of distributions in the ray space. The FrFT implements the phase space rotation. We consider the KDF averaged over the rotation group and demonstrate that it equals the WDF convolved with a smoothing kernel. We give examples of processing simple test signals, for which we evaluate the FrFT, KDF, WDF, and smoothed WDF (SWDF). We analyze the advantages of the SWDF and show examples of its application to the analysis of real RO observations.<\/jats:p>","DOI":"10.3390\/rs14225802","type":"journal-article","created":{"date-parts":[[2022,11,17]],"date-time":"2022-11-17T03:27:44Z","timestamp":1668655664000},"page":"5802","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Fractional Fourier Transform and Distributions in the Ray Space: Application for the Analysis of Radio Occultation Data"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2738-0547","authenticated-orcid":false,"given":"Michael","family":"Gorbunov","sequence":"first","affiliation":[{"name":"A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119017 Moscow, Russia"},{"name":"Hydrometeorological Research Center of Russian Federation, 123242 Moscow, Russia"}]},{"given":"Oksana","family":"Dolovova","sequence":"additional","affiliation":[{"name":"A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119017 Moscow, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.5194\/amt-4-1077-2011","article-title":"Exploring Earth\u2019s atmosphere with radio occultation: Contributions to weather, climate and space weather","volume":"4","author":"Anthes","year":"2011","journal-title":"Atmos. Meas. 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Remote Sens. Lett."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/22\/5802\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:19:56Z","timestamp":1760145596000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/22\/5802"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,17]]},"references-count":57,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["rs14225802"],"URL":"https:\/\/doi.org\/10.3390\/rs14225802","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,11,17]]}}}