{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T02:25:16Z","timestamp":1771640716915,"version":"3.50.1"},"reference-count":10,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,22]],"date-time":"2018-05-22T00:00:00Z","timestamp":1526947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Nature Science Foundation under Grant","award":["61501324"],"award-info":[{"award-number":["61501324"]}]},{"name":"the Nature Science Foundation of Tianjin under Grant","award":["14JCYBJC16100"],"award-info":[{"award-number":["14JCYBJC16100"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Cosine-modulated filter banks play a major role in digital signal processing. Sparse FIR filter banks have lower implementation complexity than full filter banks, while keeping a good performance level. This paper presents a fast design paradigm for sparse nearly perfect-reconstruction (NPR) cosine-modulated filter banks. First, an approximation function is introduced to reduce the non-convex quadratically constrained optimization problem to a linearly constrained optimization problem. Then, the desired sparse linear phase FIR prototype filter is derived through the orthogonal matching pursuit (OMP) performed under the weighted    l 2    norm. The simulation results demonstrate that the proposed scheme is an effective paradigm to design sparse NPR cosine-modulated filter banks.<\/jats:p>","DOI":"10.3390\/a11050077","type":"journal-article","created":{"date-parts":[[2018,5,23]],"date-time":"2018-05-23T03:14:24Z","timestamp":1527045264000},"page":"77","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Novel Design of Sparse Prototype Filter for Nearly Perfect Reconstruction Cosine-Modulated Filter Banks"],"prefix":"10.3390","volume":"11","author":[{"given":"Wei","family":"Xu","sequence":"first","affiliation":[{"name":"School of Electronics and Information Engineering, Tianjin Polytechnic University, Tianjin 300387, China"},{"name":"Tianjin Key Laboratory of Optoelectronic Detection Technology and System, Tianjin 300387, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8973-3160","authenticated-orcid":false,"given":"Yi","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Tianjin Polytechnic University, Tianjin 300387, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinghong","family":"Miao","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Tianjin Polytechnic University, Tianjin 300387, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaxiang","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Electronic Information and Optical Engineering, Nankai University, Tianjin 300071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Tianjin Polytechnic University, Tianjin 300387, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1109\/TBCAS.2015.2436916","article-title":"A reconfigurable sound wave decomposition filter bank for hearing aids based on nonlinear transformation","volume":"10","author":"Hang","year":"2016","journal-title":"IEEE Tran. Biomed. Circuits Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2517","DOI":"10.1109\/TSP.2014.2312326","article-title":"Optimal design of cosine modulated nonuniform linear phase FIR filter bank via both stretching and shifting frequency response of single prototype filter","volume":"62","author":"Ling","year":"2014","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1587\/transfun.E93.A.724","article-title":"A class of near shift-invariant and orientation-selective transform based on delay-less oversampled even-stacked cosine-modulated filter banks","volume":"E93.A","author":"Kyochi","year":"2010","journal-title":"IEICE Trans. Fundam. Electron. Commun. Comput. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1890","DOI":"10.1080\/00207217.2015.1006688","article-title":"Cognitive wideband spectrum sensing using cosine-modulated filter banks","volume":"102","author":"Zhao","year":"2015","journal-title":"Int. J. Electron."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1109\/TSIPN.2016.2581303","article-title":"Spectral graph wavelets and filter banks with low approximation error","volume":"2","author":"Sakiyama","year":"2016","journal-title":"IEEE Trans. Signal Inf. Proc. Over Netw."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1016\/j.jfranklin.2011.01.006","article-title":"A simple design method for the cosine-modulated filter banks using weighted constrained least square technique","volume":"348","author":"Kumar","year":"2011","journal-title":"J. Frankl. Inst. Geophys."},{"key":"ref_7","first-page":"2280","article-title":"Optimal design of cosine modulated filter banks using quantum-behaved particle swarm optimization algorithm","volume":"5","author":"Tan","year":"2011","journal-title":"Image Signal Proc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1109\/LSP.2007.906624","article-title":"Efficient design of cosine modulated filter banks based on gradient information","volume":"14","author":"Zhang","year":"2007","journal-title":"IEEE Signal Proc. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4655","DOI":"10.1109\/TIT.2007.909108","article-title":"Signal recovery from random measurements via orthogonal matching pursuit","volume":"53","author":"Tropp","year":"2007","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.1190\/1.1444219","article-title":"Hybrid l1\/l2 minimization with applications to tomography","volume":"62","author":"Bube","year":"1997","journal-title":"Geophysics"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/11\/5\/77\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:05:24Z","timestamp":1760195124000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/11\/5\/77"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,22]]},"references-count":10,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2018,5]]}},"alternative-id":["a11050077"],"URL":"https:\/\/doi.org\/10.3390\/a11050077","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,22]]}}}