{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T21:35:43Z","timestamp":1769204143854,"version":"3.49.0"},"reference-count":36,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T00:00:00Z","timestamp":1702598400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Romanian Ministry of Education and Research, CNCS\u2014UEFISCDI","award":["PCE 172 (PN-III-P4-ID-PCE2020-0713)"],"award-info":[{"award-number":["PCE 172 (PN-III-P4-ID-PCE2020-0713)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper proposes an analytical design procedure for 2D FIR circular filter banks and also a novel, computationally efficient implementation of the designed filter bank based on a polyphase structure and a block filtering approach. The component filters of the bank are designed in the frequency domain using a specific frequency transformation applied to a low-pass, band-pass and high-pass 1D prototype with a specified Gaussian shape and imposed specifications (peak frequency, bandwidth). The 1D prototype filter frequency response is derived in a closed form as a trigonometric polynomial with a specified order using Fourier series, and then it is factored. Since the design starts from a 1D prototype with a factored transfer function, the frequency response of the designed 2D filter bank components also results directly in a factored form. The designed filters have an accurate shape, with negligible distortions at a relatively low order. We present the design of two types of circular filter banks: uniform and non-uniform (dyadic). An example of image analysis with the uniform filter bank is also provided, showing that the original image can be accurately reconstructed from the sub-band images. The proposed implementation is presented for a simpler case, namely for a smaller size of the filter kernel and of the input image. Using the polyphase and block filtering approach, a convenient implementation at the system level is obtained for the designed 2D FIR filter, with a relatively low computational complexity.<\/jats:p>","DOI":"10.3390\/s23249851","type":"journal-article","created":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T11:28:07Z","timestamp":1702898887000},"page":"9851","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Analytic Design Technique for 2D FIR Circular Filter Banks and Their Efficient Implementation Using Polyphase Approach"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4775-1795","authenticated-orcid":false,"given":"Radu","family":"Matei","sequence":"first","affiliation":[{"name":"Faculty of Electronics, Telecommunications and Information Technology, \u201cGheorghe Asachi\u201d Technical University of Ia\u015fi, 700506 Ia\u015fi, Romania"},{"name":"Institute of Computer Science, Ia\u015fi Branch of the Romanian Academy, 700481 Ia\u015fi, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3322-4663","authenticated-orcid":false,"given":"Doru Florin","family":"Chiper","sequence":"additional","affiliation":[{"name":"Faculty of Electronics, Telecommunications and Information Technology, \u201cGheorghe Asachi\u201d Technical University of Ia\u015fi, 700506 Ia\u015fi, Romania"},{"name":"Technical Sciences Academy of Romania (ASTR), 700050 Ia\u015fi, Romania"},{"name":"Academy of Romanian Scientists (AOSR), 030167 Bucure\u0219ti, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,15]]},"reference":[{"key":"ref_1","unstructured":"Lu, W., and Antoniou, A. (1992). Two-Dimensional Digital Filters, CRC Press."},{"key":"ref_2","first-page":"574","article-title":"Design of variable two-dimensional FIR digital filters by McClellan transformation","volume":"56","author":"Shyu","year":"2009","journal-title":"IEEE Trans. Circ. Syst. I"},{"key":"ref_3","first-page":"167","article-title":"Design of two-dimensional zero-phase FIR digital filter by McClellan transformation and interval global optimization","volume":"60","author":"Wang","year":"2013","journal-title":"IEEE Trans. Circ. Syst. II Express Briefs"},{"key":"ref_4","first-page":"344","article-title":"Design of sharp 2D multiplier-less circularly symmetric FIR filter using harmony search algorithm and frequency transformation","volume":"3","author":"Manuel","year":"2012","journal-title":"J. Signal Inf. Proc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1326","DOI":"10.1049\/el.2015.0143","article-title":"Design of computationally efficient 2D FIR filters using sampling-kernel-based interpolation and frequency transformation","volume":"51","author":"Kim","year":"2015","journal-title":"Electron. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Pun, C.K.S., Chan, S.C., and Ho, K.L. (2001, January 6\u20139). Efficient 1D and Circular Symmetric 2D FIR Filters with Variable Cutoff Frequencies Using the Farrow Structure and Multiplier-Block. Proceedings of the IEEE International Symposium Circuits Systems ISCAS 2001, Sydney, Australia.","DOI":"10.1109\/ISCAS.2001.921132"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1109\/TCSI.2017.2724767","article-title":"Design and implementation of low complexity 2-D variable digital FIR filters using single-parameter-tunable 2-D Farrow structure","volume":"65","author":"Bindima","year":"2018","journal-title":"IEEE Trans. Circuits Syst. I Regul. Papers"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Stavrou, V.N., Tsoulos, I.G., and Mastorakis, N.E. (2021). Transformations for FIR and IIR filters\u2019 design. Symmetry, 13.","DOI":"10.3390\/sym13040533"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1109\/MSP.2017.2717498","article-title":"An easy and efficient method for synthesizing two-dimensional finite impulse response filters with improved selectivity","volume":"34","author":"Apostolov","year":"2017","journal-title":"IEEE Signal Proc. Mag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1109\/LSP.2019.2891965","article-title":"A novel 2-D FIR filter design methodology based on a Gaussian-based approximation","volume":"26","author":"Capizzi","year":"2019","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_11","first-page":"703","article-title":"Two-dimensional filters with wideband circularly symmetric frequency response","volume":"41","author":"Guillemot","year":"1994","journal-title":"IEEE Trans. Circuits Syst. II"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bindima, T., Manuel, M., and Elias, E. (2016, January 22\u201325). An efficient transformation for two dimensional circularly symmetric wideband FIR filters. Proceedings of the IEEE Region 10 Conference TENCON, Singapore.","DOI":"10.1109\/TENCON.2016.7848561"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Hung, T.Q., Tuan, H.D., and Nguyen, T.Q. (2007, January 27\u201330). Design of diamond and circular filters by semi-definite programming. Proceedings of the IEEE International Symposium on Circuits and Systems, New Orleans, LA, USA.","DOI":"10.1109\/ISCAS.2007.377969"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1109\/34.761261","article-title":"Filtering for texture classification: A comparative study","volume":"21","author":"Randen","year":"1999","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1109\/LGRS.2018.2815782","article-title":"Automatic detection of subsidence troughs in SAR interferograms based on circular Gabor filters","volume":"15","author":"Rotter","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/BF01826246","article-title":"Theory and design of two-dimensional filter banks: A review","volume":"7","author":"Lin","year":"1996","journal-title":"Multidim Syst. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1109\/TCSI.2002.1010038","article-title":"Multidimensional causal, stable, perfect reconstruction filter banks","volume":"49","author":"Basu","year":"2002","journal-title":"IEEE Trans. Circuits Syst. I Fundam. Theory Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4936","DOI":"10.1109\/TSP.2009.2027737","article-title":"Design of directional filter banks with arbitrary number of subbands","volume":"57","author":"Shi","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1109\/TIP.2010.2052267","article-title":"Nonuniform directional filter banks with arbitrary frequency partitioning","volume":"20","author":"Liang","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1109\/TSP.2006.887140","article-title":"A class of multiresolution directional filter banks","volume":"55","author":"Nguyen","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1109\/TIP.2007.891785","article-title":"Multidimensional directional filter banks and surfacelets","volume":"16","author":"Lu","year":"2007","journal-title":"IEEE Trans. Image Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s10044-021-01042-3","article-title":"Directional filter bank-based fingerprint image quality","volume":"25","author":"Hendre","year":"2022","journal-title":"Pattern Anal. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1233","DOI":"10.1080\/00207219208925793","article-title":"Fast block implementation of two-dimensional FIR digital filters by systolic arrays","volume":"73","author":"Mertzios","year":"1992","journal-title":"Int. J. Electron."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/S1077-2014(03)00021-4","article-title":"High performance 2D parallel block-filtering system for real-time imaging applications using the sharc ADSP21060","volume":"9","author":"Aziz","year":"2003","journal-title":"Real-Time Imaging"},{"key":"ref_25","unstructured":"Simoncelli, E.P., and Freeman, W.T. (1995, January 23\u201326). The steerable pyramid: A flexible architecture for multi-scale derivative computation. Proceedings of the International Conference on Image Processin, Washington, DC, USA."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"122459","DOI":"10.1109\/ACCESS.2019.2934981","article-title":"Retinex-based Laplacian pyramid method for image defogging","volume":"7","author":"Zhou","year":"2019","journal-title":"IEEE Access"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Xu, Y., Yang, X., Ling, H., and Ji, H. (2010, January 13\u201318). A new texture descriptor using multifractal analysis in multi-orientation wavelet pyramid. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, San Francisco, CA, USA.","DOI":"10.1109\/CVPR.2010.5540217"},{"key":"ref_28","first-page":"5512615","article-title":"Hyperspectral and multispectral classification for coastal wetland using depthwise feature interaction network","volume":"60","author":"Gao","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/j.neunet.2023.10.043","article-title":"Multi-scale feature selection network for lightweight image super-resolution","volume":"169","author":"Li","year":"2023","journal-title":"Neural Netw."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"120615","DOI":"10.1016\/j.eswa.2023.120615","article-title":"Hyperspectral pathology image classification using dimension-driven multi-path attention residual network","volume":"230","author":"Zhang","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Li, L., Lv, M., Jia, Z., and Ma, H. (2023). Sparse representation-based multi-focus image fusion method via local energy in shearlet domain. Sensors, 23.","DOI":"10.3390\/s23062888"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1629","DOI":"10.1109\/TCSI.2021.3139141","article-title":"A class of directional zero-phase 2D filters designed using analytical approach","volume":"69","author":"Matei","year":"2022","journal-title":"IEEE Trans. Circuits Syst. I Regular Papers"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/s10470-023-02152-0","article-title":"Design and applications of adjustable 2D digital filters with elliptical and circular symmetry","volume":"114","author":"Matei","year":"2023","journal-title":"Analog. Integr. Circuits Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Matei, R. (2020, January 23\u201325). Analytic Design of Uniform Circular Filter Banks. Proceedings of the 24th IEEE Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA), Pozna\u0144, Poland.","DOI":"10.23919\/SPA50552.2020.9241281"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Matei, R. (2021, January 9\u201311). Efficient Design Procedure for Circular Filter Banks. Proceedings of the IEEE 63rd International Midwest Symposium on Circuits and Systems (MWSCAS), East Lansing, MI, USA.","DOI":"10.1109\/MWSCAS47672.2021.9531686"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Chiper, D.F., and Matei, R. (2023, January 29\u201330). Polyphase Implementation for Gaussian 2D FIR Filters with Circular Symmetry. Proceedings of the 15th International Conference on Electronics, Computers and Artificial Intelligence ECAI 2023, Bucharest, Romania.","DOI":"10.1109\/ECAI58194.2023.10194150"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/24\/9851\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:39:39Z","timestamp":1760132379000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/24\/9851"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,15]]},"references-count":36,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["s23249851"],"URL":"https:\/\/doi.org\/10.3390\/s23249851","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,15]]}}}