{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T02:34:09Z","timestamp":1769308449472,"version":"3.49.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,8,27]],"date-time":"2023-08-27T00:00:00Z","timestamp":1693094400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,8,27]],"date-time":"2023-08-27T00:00:00Z","timestamp":1693094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2024,1]]},"DOI":"10.1007\/s00034-023-02485-1","type":"journal-article","created":{"date-parts":[[2023,8,27]],"date-time":"2023-08-27T15:01:53Z","timestamp":1693148513000},"page":"470-494","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Gabor Phase Retrieval in the Generalized Paley\u2013wiener Space"],"prefix":"10.1007","volume":"43","author":[{"given":"Qingyue","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liping","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenli","family":"Guo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bei","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,8,27]]},"reference":[{"issue":"22","key":"2485_CR1","doi-asserted-by":"publisher","first-page":"1801","DOI":"10.1364\/OL.19.001801","volume":"19","author":"S Abe","year":"1994","unstructured":"S. Abe, J.T. Sheridan, Optical operations on wave functions as the abelian subgroups of the special affine Fourier transformation. Opt. Lett. 19(22), 1801\u20131803 (1994)","journal-title":"Opt. Lett."},{"issue":"6","key":"2485_CR2","first-page":"1","volume":"27","author":"R Alaifari","year":"2021","unstructured":"R. Alaifari, M. Wellershok, Stability estimates for phase retrieval from discrete Gabor measurements. J. Fourier Anal. Appl. 27(6), 1\u201331 (2021)","journal-title":"J. Fourier Anal. Appl."},{"issue":"1","key":"2485_CR3","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/j.acha.2020.08.003","volume":"50","author":"R Alaifari","year":"2021","unstructured":"R. Alaifari, M. Wellershoff, Uniqueness of STFT phase retrieval for bandlimited functions. Appl. Comput. Harmon. Anal. 50(1), 34\u201348 (2021)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"9","key":"2485_CR4","first-page":"1","volume":"28","author":"R Alaifari","year":"2022","unstructured":"R. Alaifari, M. Wellershoff, Phase retrieval from sampled Gabor transform magnitudes: counterexamples. J. Fourier Anal. Appl. 28(9), 1\u20138 (2022)","journal-title":"J. Fourier Anal. Appl."},{"issue":"11","key":"2485_CR5","doi-asserted-by":"publisher","first-page":"3084","DOI":"10.1109\/78.330368","volume":"42","author":"L Almeida","year":"1994","unstructured":"L. Almeida, The fractional Fourier transform and time\u2013frequency representations. IEEE Tran. Signal Process 42(11), 3084\u20133091 (1994)","journal-title":"IEEE Tran. Signal Process"},{"issue":"3","key":"2485_CR6","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1137\/0516043","volume":"16","author":"L Auslander","year":"1985","unstructured":"L. Auslander, R. Tolimieri, Radar ambiguity functions and group theory. SIAM J. Math. Anal. 16(3), 577\u2013601 (1985)","journal-title":"SIAM J. Math. Anal."},{"issue":"1","key":"2485_CR7","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.acha.2017.07.002","volume":"47","author":"A Bhandari","year":"2019","unstructured":"A. Bhandari, A. Zayed, Shift-invariant and sampling spaces associated with the special affine Fourier transform. Appl. Comput. Harmon. Anal. 47(1), 30\u201352 (2019)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"2485_CR8","volume-title":"The Fourier Transform and its Applications","author":"RN Bracewell","year":"1986","unstructured":"R.N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill College, New York, 1986)"},{"issue":"1309","key":"2485_CR9","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1098\/rspa.1961.0109","volume":"262","author":"L Bragg","year":"1961","unstructured":"L. Bragg, The Rutherford memorial lecture 1960. The development of X-ray analysis. Proc. R. Soc. Lond. Ser. A 262(1309), 145\u2013158 (1961)","journal-title":"Proc. R. Soc. Lond. Ser. A"},{"issue":"1","key":"2485_CR10","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.acha.2021.04.004","volume":"55","author":"W Chen","year":"2021","unstructured":"W. Chen, Z. Fu, L. Grafakos, Y. Wu, Fractional Fourier transforms on $$L^{p}$$ and applications. Appl. Comput. Harmon. Anal. 55(1), 71\u201396 (2021)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"2485_CR11","first-page":"275","volume":"231","author":"J Dainty","year":"1987","unstructured":"J. Dainty, J. Fienup, Phase retrieval and image reconstruction for astronomy. Image Recove. Theory Appl. 231, 275 (1987)","journal-title":"Image Recove. Theory Appl."},{"issue":"2","key":"2485_CR12","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1109\/TASSP.1984.1164317","volume":"32","author":"D Griffin","year":"1984","unstructured":"D. Griffin, J. Lim, Signal estimation from modified short-time Fourier transform. IEEE Trans. Acoust. Speech Signal Process. 32(2), 236\u2013243 (1984)","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"2485_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0003-1","volume-title":"Foundations of Time\u2013Frequency Analysis","author":"K Grochenig","year":"2001","unstructured":"K. Grochenig, Foundations of Time\u2013Frequency Analysis (Springer Science Business Media, Berlin, 2001)"},{"issue":"1","key":"2485_CR14","first-page":"173","volume":"62","author":"P Grohs","year":"2022","unstructured":"P. Grohs, L. Liehr, Injectivity of Gabor phase retrieval from lattice measurements. Appl. Comput. Harmon. Anal. 62(1), 173\u2013193 (2022)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"2485_CR15","volume-title":"Optics","author":"E Hecht","year":"1974","unstructured":"E. Hecht, A. Zajac, Optics (Addison-Wesley, Boston, 1974)"},{"issue":"12","key":"2485_CR16","doi-asserted-by":"publisher","first-page":"3316","DOI":"10.1364\/JOSAA.14.003316","volume":"14","author":"J Hua","year":"1997","unstructured":"J. Hua, L. Liu, G.Q. Li, Extended fractional Fourier transforms. J. Opt. Soc. Am. A 14(12), 3316\u20133322 (1997)","journal-title":"J. Opt. Soc. Am. A"},{"issue":"3","key":"2485_CR17","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1016\/j.acha.2014.01.003","volume":"37","author":"P Jaming","year":"2014","unstructured":"P. Jaming, Uniqueness results in an extension of Pauli\u2019s phase retrieval problem. Appl. Comput. Harmon. Anal. 37(3), 413\u2013441 (2014)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"4","key":"2485_CR18","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/BF01259373","volume":"5","author":"P Jaming","year":"1999","unstructured":"P. Jaming, Phase retrieval techniques for radar ambiguity problems. J. Fourier Anal. Appl. 5(4), 309\u2013329 (1999)","journal-title":"J. Fourier Anal. Appl."},{"issue":"3","key":"2485_CR19","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1364\/JOSAA.7.000394","volume":"7","author":"R Millane","year":"1990","unstructured":"R. Millane, Phase retrieval in crystallography and optics. J. Opt. Soc. Am. A 7(3), 394\u2013411 (1990)","journal-title":"J. Opt. Soc. Am. A"},{"issue":"4","key":"2485_CR20","doi-asserted-by":"publisher","first-page":"986","DOI":"10.1109\/TASSP.1983.1164162","volume":"31","author":"S Nawab","year":"1983","unstructured":"S. Nawab, T. Quatieri, J. Lim, Signal reconstruction from short time Fourier transform magnitude. IEEE Trans. Acoust. Speech Signal Process. 31(4), 986\u2013998 (1983)","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"2485_CR21","volume-title":"Fundamentals of Speech Recognition","author":"L Rabiner","year":"1993","unstructured":"L. Rabiner, B. Juang, Fundamentals of Speech Recognition (Prentice-Hall Inc, Hoboken, 1993)"},{"key":"2485_CR22","volume-title":"Real and Complex Analysis","author":"W Rudin","year":"1970","unstructured":"W. Rudin, Real and Complex Analysis (McGraw-Hill Inc, New York, 1970)"},{"key":"2485_CR23","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/s00034-013-9633-0","volume":"33","author":"V Stojanovic","year":"2014","unstructured":"V. Stojanovic, V. Filipovic, Adaptive input design for identification of output error model with constrained output. Circ. Syst. Signal Pr. 33, 97\u2013113 (2014)","journal-title":"Circ. Syst. Signal Pr."},{"issue":"3","key":"2485_CR24","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1002\/rnc.3319","volume":"26","author":"V Stojanovic","year":"2015","unstructured":"V. Stojanovic, N. Nedic, Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non-Gaussian noise. Int. J. Robust Nonlin. 26(3), 445\u2013460 (2015)","journal-title":"Int. J. Robust Nonlin."},{"issue":"13","key":"2485_CR25","doi-asserted-by":"publisher","first-page":"6676","DOI":"10.1016\/j.apm.2016.02.014","volume":"40","author":"V Stojanovic","year":"2016","unstructured":"V. Stojanovic, N. Nedic, D. Prsic, L. Dubonjic, Optimal experiment design for identification of ARX models with constrained output in non-Gaussian noise. Appl. Math. Model. 40(13), 6676\u20136689 (2016)","journal-title":"Appl. Math. Model."},{"key":"2485_CR26","unstructured":"M. Wellershoff, Injectivity of sampled Gabor phase retrieval in spaces with general integrability conditions. arXiv:2112.10136 (2021)"},{"issue":"1","key":"2485_CR27","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.optcom.2012.10.040","volume":"290","author":"L Xiao","year":"2013","unstructured":"L. Xiao, W. Sun, Sampling theorems for signals periodic in the linear canonical transform domain. Opt. Commun. 290(1), 14\u201318 (2013)","journal-title":"Opt. Commun."},{"issue":"5","key":"2485_CR28","doi-asserted-by":"publisher","first-page":"2613","DOI":"10.1016\/j.ijleo.2015.11.211","volume":"127","author":"Z Xiyang","year":"2016","unstructured":"Z. Xiyang, W. Deyun, Z. Wei, A generalized convolution theorem for the special affine Fourier transform and its application to filtering. Optik 127(5), 2613\u20132616 (2016)","journal-title":"Optik"},{"key":"2485_CR29","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1090\/S0002-9947-1978-0493077-1","volume":"243","author":"R Zalik","year":"1978","unstructured":"R. Zalik, On approximation by shifts and a theorem of Wiener. Trans. Am. Math. Soc. 243, 299\u2013308 (1978)","journal-title":"Trans. Am. Math. Soc."},{"key":"2485_CR30","volume-title":"Advances in Shannon\u2019s sampling theory","author":"AI Zayed","year":"1993","unstructured":"A.I. Zayed, Advances in Shannon\u2019s sampling theory (Taylor Francis Group, Milton Park, 1993)"}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-023-02485-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-023-02485-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-023-02485-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T22:05:46Z","timestamp":1705010746000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-023-02485-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,27]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,1]]}},"alternative-id":["2485"],"URL":"https:\/\/doi.org\/10.1007\/s00034-023-02485-1","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,27]]},"assertion":[{"value":"12 October 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 August 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 August 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 August 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}