{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T20:52:30Z","timestamp":1758401550670,"version":"3.37.3"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T00:00:00Z","timestamp":1651017600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T00:00:00Z","timestamp":1651017600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SPP 1798"],"award-info":[{"award-number":["SPP 1798"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006221","name":"United States - Israel Binational Science Foundation","doi-asserted-by":"publisher","award":["2017698"],"award-info":[{"award-number":["2017698"]}],"id":[{"id":"10.13039\/100006221","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s10444-022-09941-7","type":"journal-article","created":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T11:05:27Z","timestamp":1651057527000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Randomized continuous frames in time-frequency analysis"],"prefix":"10.1007","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3004-7515","authenticated-orcid":false,"given":"Ron","family":"Levie","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haim","family":"Avron","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,4,27]]},"reference":[{"issue":"1","key":"9941_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/aphy.1993.1016","volume":"222","author":"S Ali","year":"1993","unstructured":"Ali, S., Antoine, J., Gazeau, J.: Continuous frames in Hilbert space. Ann. Phys. 222(1), 1\u201337 (1993)","journal-title":"Ann. Phys."},{"key":"9941_CR2","volume-title":"An Invitation to Operator Theory","author":"CD Aliprantis","year":"2002","unstructured":"Aliprantis, C.D.: An Invitation to Operator Theory. American Mathematical Society, Rhode Island (2002)"},{"issue":"1","key":"9941_CR3","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1016\/j.jmaa.2006.02.012","volume":"325","author":"P Balazs","year":"2007","unstructured":"Balazs, P.: Basic definition and properties of Bessel multipliers. J. Math. Anal. Appl. 325(1), 571\u2013585 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"9941_CR4","doi-asserted-by":"crossref","unstructured":"Balazs, P., Bayer, D., Rahimi, A.: Multipliers for continuous frames in Hilbert spaces. Journal of Physics A: Mathematical and Theoretical 45(24) (2012)","DOI":"10.1088\/1751-8113\/45\/24\/244023"},{"key":"9941_CR5","doi-asserted-by":"crossref","unstructured":"Balazs, P., Gr\u00f6chenig, K., Speckbacher, M.: Kernel theorems in coorbit theory. arXiv:1903.02961, [math.FA] (2019)","DOI":"10.1090\/btran\/42"},{"issue":"1","key":"9941_CR6","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1109\/TASL.2009.2023164","volume":"18","author":"P Balazs","year":"2010","unstructured":"Balazs, P., Laback, B., Eckel, G., Deutsch, W.A.: Time-frequency sparsity by removing perceptually irrelevant components using a simple model of simultaneous masking. Trans. Audio Speech Lang. Proc. 18(1), 34\u201349 (2010). https:\/\/doi.org\/10.1109\/TASL.2009.2023164","journal-title":"Trans. Audio Speech Lang. Proc."},{"issue":"1","key":"9941_CR7","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1215\/ijm\/1403534485","volume":"57","author":"RF Bass","year":"2013","unstructured":"Bass, R.F., Gr\u00f6chenig, K.: Relevant sampling of band-limited functions. Ill. J. Math. 57 (1), 43\u201358 (2013). https:\/\/doi.org\/10.1215\/ijm\/1403534485","journal-title":"Ill. J. Math."},{"issue":"2","key":"9941_CR8","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1016\/j.acha.2005.02.004","volume":"19","author":"J Cand\u00e8s","year":"2005","unstructured":"Cand\u00e8s, J., Donoho, D.L.: Continuous curvelet transform: II. discretization and frames. Appl. Comput. Harmon. Anal. 19(2), 198\u2013222 (2005)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"9941_CR9","volume-title":"An Introduction to Frames and Riesz","author":"O Christensen","year":"2002","unstructured":"Christensen, O.: An Introduction to Frames and Riesz. Birkh\u00e4user, Bases (2002)"},{"issue":"1","key":"9941_CR10","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1109\/TASSP.1980.1163353","volume":"28","author":"R Crochiere","year":"1980","unstructured":"Crochiere, R.: A weighted overlap-add method of short-time fourier analysis\/synthesis. IEEE Trans. Acoust. Speech Sig. Process. 28(1), 99\u2013102 (1980). https:\/\/doi.org\/10.1109\/TASSP.1980.1163353","journal-title":"IEEE Trans. Acoust. Speech Sig. Process."},{"issue":"02","key":"9941_CR11","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1142\/S021969130800229X","volume":"06","author":"S Dahlke","year":"2008","unstructured":"Dahlke, S., Kutyniok, G., Maass, P., Sagiv, C., Stark, H.G., Teschke, G.: The uncertainty principle associated with the continuous shearlet transform. International Journal of Wavelets Multiresolution and Information Processing 06(02), 157\u2013181 (2008)","journal-title":"International Journal of Wavelets Multiresolution and Information Processing"},{"key":"9941_CR12","doi-asserted-by":"crossref","unstructured":"Daubechies, I.: Ten lectures on wavelets SIAM: Society for industrial and applied mathematics (1992)","DOI":"10.1137\/1.9781611970104"},{"issue":"3","key":"9941_CR13","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1093\/biomet\/81.3.425","volume":"81","author":"D Donoho","year":"1994","unstructured":"Donoho, D., Johnstone, J.: Ideal spatial adaptation by wavelet shrinkage. Biometrika 81(3), 425\u2013455 (1994). https:\/\/doi.org\/10.1093\/biomet\/81.3.425","journal-title":"Biometrika"},{"issue":"2","key":"9941_CR14","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1111\/j.2517-6161.1995.tb02032.x","volume":"57","author":"DL Donoho","year":"1995","unstructured":"Donoho, D.L., Johnstone, I.M., Kerkyacharian, G., Picard, D.: Wavelet shrinkage: Asymptopia. J. R. Stat. Soc. Series B (Methodological) 57 (2), 301\u2013369 (1995)","journal-title":"J. R. Stat. Soc. Series B (Methodological)"},{"key":"9941_CR15","doi-asserted-by":"crossref","unstructured":"Driedger, J., M\u00fcller, M.: A review of time-scale modification of music signals. Applied Sciences 12(2) (2016)","DOI":"10.3390\/app6020057"},{"key":"9941_CR16","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/0022-1236(76)90079-3","volume":"21","author":"M Duflo","year":"1976","unstructured":"Duflo, M., Moore, C.: On the regular representation of a nonunimodular locally compact group. J. Funct. Anal. 21, 209\u2013243 (1976)","journal-title":"J. Funct. Anal."},{"key":"9941_CR17","unstructured":"Evangelista, G., D\u00f6rfler, M., Matusiak, E.: Arbitrary phase vocoders by means of warping. Musica\/Tecnologia 7(0) (2013)"},{"issue":"17","key":"9941_CR18","first-page":"A791","volume":"290","author":"HG Feichtinger","year":"1980","unstructured":"Feichtinger, H.G.: Un espace de banach de distributions temp\u00e9r\u00e9es sur les groupes localement compacts ab\u00e9liens. C. R. Acad. Sci. Paris S er 290 (17), A791\u2013A794 (1980)","journal-title":"C. R. Acad. Sci. Paris S er"},{"key":"9941_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jat.2018.09.009","volume":"240","author":"H F\u00fchr","year":"2019","unstructured":"F\u00fchr, H., Xian, J.: Relevant sampling in finitely generated shift-invariant spaces. J. Approx. Theory 240, 1\u201315 (2019). https:\/\/doi.org\/10.1016\/j.jat.2018.09.009","journal-title":"J. Approx. Theory"},{"key":"9941_CR20","doi-asserted-by":"publisher","DOI":"10.1515\/9781400882427","volume-title":"Harmonic analysis in phase space. (AM-122)","author":"GB Folland","year":"1989","unstructured":"Folland, G.B.: Harmonic analysis in phase space. (AM-122). Princeton University Press, Princeton (1989)"},{"key":"9941_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/b104912","volume-title":"Abstract Harmonic Analysis of Continuous Wavelet Transforms","author":"H F\u00fchr","year":"2005","unstructured":"F\u00fchr, H.: Abstract Harmonic Analysis of Continuous Wavelet Transforms. Springer, Berlin (2005)"},{"key":"9941_CR22","doi-asserted-by":"crossref","unstructured":"Gr\u00f6chenig, K.: Foundations of Time-Frequency Analysis. Birkh\u00e4user, Basel (2001)","DOI":"10.1007\/978-1-4612-0003-1"},{"issue":"4","key":"9941_CR23","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1137\/0515056","volume":"15","author":"A Grossmann","year":"1984","unstructured":"Grossmann, A., Morlet, J.: Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM J. Math. Anal. 15(4), 723\u2013736 (1984)","journal-title":"SIAM J. Math. Anal."},{"issue":"10","key":"9941_CR24","doi-asserted-by":"publisher","first-page":"2473","DOI":"10.1063\/1.526761","volume":"26","author":"A Grossmann","year":"1985","unstructured":"Grossmann, A., Morlet, J., Paul, T.: Transforms associated with square integrable group representations i. general results. J. Math. Phys. 26 (10), 2473\u20132479 (1985)","journal-title":"J. Math. Phys."},{"key":"9941_CR25","doi-asserted-by":"publisher","unstructured":"Guo, Q., Yu, S., Chen, X., Liu, C., Wei, W.: Shearlet-based image denoising using bivariate shrinkage with intra-band and opposite orientation dependencies. In: 2009 International Joint Conference on Computational Sciences and Optimization. https:\/\/doi.org\/10.1109\/CSO.2009.218, vol. 1, pp 863\u2013866 (2009)","DOI":"10.1109\/CSO.2009.218"},{"key":"9941_CR26","volume-title":"C*-algebras and Numerical Analysis","author":"R Hagen","year":"2001","unstructured":"Hagen, R., Roch, S., Silbermann, B.: C*-algebras and Numerical Analysis. CRC Press, Boca Raton (2001)"},{"issue":"3","key":"9941_CR27","doi-asserted-by":"publisher","first-page":"975","DOI":"10.1016\/j.acha.2018.03.002","volume":"47","author":"N Holighaus","year":"2019","unstructured":"Holighaus, N., Wiesmeyr, C., Balazs, P.: Continuous warped time-frequency representations\u2014coorbit spaces and discretization. Appl. Comput. Harmon. Anal. 47(3), 975\u20131013 (2019)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"9941_CR28","volume-title":"The Analysis of Linear Partial Differential Operators, vol. I","author":"L H\u00f6rmander","year":"1983","unstructured":"H\u00f6rmander, L.: The Analysis of Linear Partial Differential Operators, vol. I. Springer, Berlin (1983)"},{"key":"9941_CR29","first-page":"201","volume":"59","author":"C Kalisa","year":"1993","unstructured":"Kalisa, C., Torr\u00e9sani, B.: N-dimensional affine Weyl-Heisenberg wave. Annales de l\u2019Institut Henri Poincare Physique Theorique 59, 201\u2013236 (1993)","journal-title":"Annales de l\u2019Institut Henri Poincare Physique Theorique"},{"key":"9941_CR30","doi-asserted-by":"crossref","unstructured":"Laroche, J., Dolson, M.: Phase-vocoder: about this phasiness business. In: Proceedings of 1997 Workshop on Applications of Signal Processing to Audio and Acoustics, pp. 4 pp.\u2013 (1997)","DOI":"10.1109\/ASPAA.1997.625603"},{"issue":"3","key":"9941_CR31","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1109\/89.759041","volume":"7","author":"J Laroche","year":"1999","unstructured":"Laroche, J., Dolson, M.: Improved phase vocoder time-scale modification of audio. Trans. Speech Audio Process. 7(3), 323\u2013332 (1999)","journal-title":"Trans. Speech Audio Process."},{"key":"9941_CR32","unstructured":"Levie, R., Avron, H.: Randomized signal processing with continuous frames. arXiv:1808.08810 [math.NA] (2018)"},{"key":"9941_CR33","first-page":"73","volume":"7","author":"M Liuni","year":"2013","unstructured":"Liuni, M., Roebel, A.: Phase vocoder and beyond. Music\/Technology 7, 73\u201389 (2013)","journal-title":"Music\/Technology"},{"key":"9941_CR34","doi-asserted-by":"crossref","unstructured":"Majdak, P., Bal\u00e1zs, P., Kreuzer, W., D\u00f6rfler, M.: A time-frequency method for increasing the signal-to-noise ratio in system identification with exponential sweeps. 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 3812\u20133815 (2011)","DOI":"10.1109\/ICASSP.2011.5947182"},{"key":"9941_CR35","unstructured":"Matz, G., Hlawatsch, F. In: Boashas, B. (ed.) : Time-Frequency Transfer Function Calculus Of Linear Time-Varying Systems, chapter 4.7 in Time-Frequency Signal Analysis And Processing: A Comprehensive Reference, pp 135\u2013144. Elsevie, Oxford (2003)"},{"key":"9941_CR36","doi-asserted-by":"publisher","first-page":"1550","DOI":"10.1109\/TASL.2013.2255274","volume":"21","author":"A Olivero","year":"2013","unstructured":"Olivero, A., Torr\u00e9sani, B., Kronland-Martinet, R.: A class of algorithms for time-frequency multiplier estimation. IEEE Transactions on AudioSpeech, and Language Processing 21, 1550\u20131559 (2013)","journal-title":"IEEE Transactions on AudioSpeech, and Language Processing"},{"key":"9941_CR37","doi-asserted-by":"publisher","first-page":"2199","DOI":"10.1109\/TASLP.2017.2750767","volume":"25","author":"ES Ottosen","year":"2017","unstructured":"Ottosen, E.S., D\u00f6rfler, M.: A phase vocoder based on nonstationary Gabor frames. IEEE\/ACM Transactions on Audio Speech, and Language Processing 25, 2199\u20132208 (2017)","journal-title":"IEEE\/ACM Transactions on Audio Speech, and Language Processing"},{"issue":"1","key":"9941_CR38","doi-asserted-by":"publisher","first-page":"124270","DOI":"10.1016\/j.jmaa.2020.124270","volume":"491","author":"D Patel","year":"2020","unstructured":"Patel, D., Sampath, S.: Random sampling in reproducing kernel subspaces of lp(rn). J. Math. Anal. Appl. 491(1), 124270 (2020). https:\/\/doi.org\/10.1016\/j.jmaa.2020.124270","journal-title":"J. Math. Anal. Appl."},{"issue":"2","key":"9941_CR39","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1090\/S0002-9947-1938-1501970-8","volume":"44","author":"BJ Pettis","year":"1938","unstructured":"Pettis, B.J.: On integration in vector spaces. Trans. Am. Math. Soc. 44(2), 277\u2013304 (1938)","journal-title":"Trans. Am. Math. Soc."},{"issue":"3","key":"9941_CR40","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1109\/TASSP.1976.1162810","volume":"24","author":"M Portnoff","year":"1976","unstructured":"Portnoff, M.: Implementation of the digital phase vocoder using the fast Fourier transform. IEEE Transactions on Acoustics Speech, and Signal Processing 24(3), 243\u2013248 (1976). https:\/\/doi.org\/10.1109\/TASSP.1976.1162810","journal-title":"IEEE Transactions on Acoustics Speech, and Signal Processing"},{"key":"9941_CR41","doi-asserted-by":"crossref","unstructured":"Pr\u016f\u0161a, Z., Holighaus, N.: Phase vocoder done right. In: Proceedings of 25th European Signal Processing Conference (EUSIPCO-2017), pp. 1006\u20131010. Kos (2017)","DOI":"10.23919\/EUSIPCO.2017.8081353"},{"issue":"2","key":"9941_CR42","first-page":"170","volume":"12","author":"A Rahimi","year":"2006","unstructured":"Rahimi, A., Najati, A., Dehghan, Y.N.: Continuous frame in Hilbert spaces. Methods Funct. Anal. Topology 12(2), 170\u2013182 (2006)","journal-title":"Methods Funct. Anal. Topology"},{"key":"9941_CR43","unstructured":"Smith, J.O.: Mathematics of the Discrete Fourier Transform (DFT) W3K Publishing (2007)"},{"issue":"2","key":"9941_CR44","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1016\/j.acha.2011.11.001","volume":"33","author":"D Stoeva","year":"2012","unstructured":"Stoeva, D., Balazs, P.: Invertibility of multipliers. Appl. Comput. Harmon. Anal. 33(2), 292\u2013299 (2012)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"5","key":"9941_CR45","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.1063\/1.529325","volume":"32","author":"B Torr\u00e9sani","year":"1991","unstructured":"Torr\u00e9sani, B.: Wavelets associated with representations of the affine Weyl\u2013Heisenberg group. J. Math. Phys. 32(5), 1273\u20131279 (1991). https:\/\/doi.org\/10.1063\/1.529325","journal-title":"J. Math. Phys."},{"issue":"2","key":"9941_CR46","first-page":"215","volume":"56","author":"B Torr\u00e9sani","year":"1992","unstructured":"Torr\u00e9sani, B.: Time-frequency representations: wavelet packets and optimal decomposition. Annales de l\u2019Institut Henri Poincare Physique Theorique 56(2), 215\u2013234 (1992). https:\/\/hal.archives-ouvertes.fr\/hal-01280027","journal-title":"Annales de l\u2019Institut Henri Poincare Physique Theorique"},{"key":"9941_CR47","unstructured":"Velasco, G.A.: Relevant sampling of the short-time fourier transform of time-frequency localized functions. arXiv:1707.09634 [math.FA] (2017)"},{"key":"9941_CR48","volume-title":"Fourier Analysis and its Applications","author":"A Vretbladr","year":"2000","unstructured":"Vretbladr, A.: Fourier Analysis and its Applications. Springer, Berlin (2000)"},{"key":"9941_CR49","doi-asserted-by":"publisher","DOI":"10.1002\/9781119991298","volume-title":"DAFX: Digital Audio Effects","author":"U Zolzer","year":"2011","unstructured":"Zolzer, U.: DAFX: Digital Audio Effects, 2nd edn. Wiley, Hoboken (2011)","edition":"2nd edn."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-022-09941-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10444-022-09941-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-022-09941-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,23]],"date-time":"2024-09-23T02:16:12Z","timestamp":1727057772000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10444-022-09941-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,27]]},"references-count":49,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["9941"],"URL":"https:\/\/doi.org\/10.1007\/s10444-022-09941-7","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"type":"print","value":"1019-7168"},{"type":"electronic","value":"1572-9044"}],"subject":[],"published":{"date-parts":[[2022,4,27]]},"assertion":[{"value":"24 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 March 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 April 2022","order":3,"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 no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of interest"}}],"article-number":"25"}}