Abstract
This article presents a rapidly converging optimization technique using a single parameter for designing non-uniform cosine modulated filter banks (CMFBS). The non-uniform cosine modulated filter banks are derived from closed-form uniform cosine modulated filter banks by merging the relevant bandpass filters based on given decimation factors. In this proposed method, the cut-off frequency of the prototype filter is varied through analytically calculated step size using control parameters so that the filter coefficients at quadrature frequency are approximately equal to 0.707 and the formulated objective function is satisfied with the prescribed tolerance. Simulation results demonstrate that the proposed algorithm achieves superior performance, with amplitude distortion levels significantly outperforming existing methods in the literature, reaching as low as 2.4483 × 10⁻4. For the prototype filter design, a constrained equiripple finite impulse response (FIR) digital filter is employed, with the roll-off factor and error ratio chosen based on a stopband attenuation, a passband attenuation and a filter order. The results highlight the proposed algorithm’s effectiveness for high-quality reconstruction of speech signals, particularly in speech coding and enhancement, as well as ECG signals. This makes the method highly versatile and suitable for various practical applications, including sub-band coding of real-time and near real-time signals.











Similar content being viewed by others
Data availability
The data that support the findings of this study are openly available in PhysioBank ATM at https://archive.physionet.org/cgi-bin/atm/ATM.
References
PP Vaidyanathan, (1993) “Multirate Systems and Filter Banks,” Accessed: Oct. 11, 2022. [Online]. Available: https://resolver.caltech.edu/CaltechAUTHORS:20210611-123235747
Maciej Serda et al., (1999) “Non-uniform filterbank bandwidth allocation for system modeling subband adaptive filters,” ICASSP, IEEE Int Conf Acoust Speech Signal Process Proc 3(1)1473–1476
Creusere CD, Mitra SK (1995) A Simple Method for Designing High-Quality Prototype Filters for M-Band Pseudo QMF Banks. IEEE Trans Signal Process 43(4):1005–1007. https://doi.org/10.1109/78.376856
Cruz-Roldán F, Amo-López P, Maldonado-Bascón S, Lawson SS (2002) An efficient and simple method for designing prototype filters for cosine-modulated pseudo-QMF banks. IEEE Signal Process Lett 9(1):29–31. https://doi.org/10.1109/97.988722
Bergen SWA, Antoniou A (2007) An efficient closed-form design method for cosine-modulated filter banks using window functions. Signal Process 87(5):811–823. https://doi.org/10.1016/J.SIGPRO.2006.08.003
Kumar A, Singh GK, Anand RS (2011) An improved closed form design method for the cosine modulated filter banks using windowing technique. Appl Soft Comput 11(3):3209–3217. https://doi.org/10.1016/J.ASOC.2010.12.023
Cruz-Roldán F, Bravo-Santos ÁM, Martín-Martín P, Jiménez-Martínez R (2003) Design of multi-channel near-perfect-reconstruction transmultiplexers using cosine-modulated filter banks. Signal Process 83(5):1079–1091. https://doi.org/10.1016/S0165-1684(02)00508-X
Jain A, Saxena R, Saxena SC (2006) An improved and simplified design of cosine-modulated pseudo-QMF filterbanks. Digit Signal Process 16(3):225–232. https://doi.org/10.1016/J.DSP.2005.11.001
J Li, TQ Nguyen, and S Tantaratana, (1994) “A simple design method for nonuniform multirate filter banks,” Conf Rec Asilomar Conf Signals Syst Comput 2 1015–1019. https://doi.org/10.1109/ACSSC.1994.471613
Xie XM, Chan SC, Yuk TI (2006) Design of linear-phase recombination nonuniform filter banks. IEEE Trans Signal Process 54(7):2809–2814. https://doi.org/10.1109/TSP.2006.874400
Liang L, Shi G, Xie X (2011) Nonuniform directional filter banks with arbitrary frequency partitioning. IEEE Trans Image Process 20(1):283–288. https://doi.org/10.1109/TIP.2010.2052267
A Eghbali, H Johansson, and P Löwenborg, (2010) “Reconfigurable nonuniform transmultiplexers based on uniform filter banks,” ISCAS 2010 - 2010 IEEE Int Symp Circuits Syst Nano-Bio Circuit Fabr Syst 2123–2126. https://doi.org/10.1109/ISCAS.2010.5537067
SC Chan, XM Xie, and TI Yuk, (2000) “Theory and design of a class of cosine-modulated non-uniform filter banks,” ICASSP, IEEE Int Conf Acoust Speech Signal Process Proc 1, 504–507. https://doi.org/10.1109/ICASSP.2000.862028
G Shi, X Xie, X Chen, and W Zhong, (2006) “Recent advances and new design method in nonuniform filter banks,” 2006 Int Conf Commun Circuits Syst ICCCAS, Proc 1 211–215. https://doi.org/10.1109/ICCCAS.2006.284620
Abo-Zahhad M (2003) Current state and future directions of multirate filter banks and their applications. Digit Signal Process A Rev J 13(3):495–518. https://doi.org/10.1016/S1051-2004(02)00023-4
Yin SS, Chan SC, Tsui KM (2008) “On the design of nearly-PR and PR FIR cosine modulated filter banks having approximate cosine-rolloff transition band”, IEEE Trans. Circuits Syst II Express Briefs 55(6):571–575. https://doi.org/10.1109/TCSII.2007.916733
Cruz-Roldán F, Martín-Martín P, Sáez-Landete J, Blanco-Velasco M, Saramäki T (2009) “A fast windowing-based technique exploiting spline functions for designing modulated filter banks”, IEEE Trans. Circuits Syst I Regul Pap 56(1):168–178. https://doi.org/10.1109/TCSI.2008.925350
Lu WS, Saramäki T, Bregović R (2004) “Design of practically perfect-reconstruction cosine-modulated filter banks: A second-order cone programming approach”, IEEE Trans. Circuits Syst I Regul Pap 51(3):552–563. https://doi.org/10.1109/TCSI.2003.822555
Akkarakaran S, Vaidyanathan PP (1999) New results and open problems on nonuniform filter-banks. IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258) vol.3. Phoenix, AZ, USA, pp. 1501–1504. https://doi.org/10.1109/ICASSP.1999.756268
S Akkarakaran and PP Vaidyanathan, (2003) “Nonuniform Filter Banks: New Results and open Problems,” Stud Comput Math. 10(C)259–301. https://doi.org/10.1016/S1570-579X(03)80038-1
BG Lee, (1995) “A Design of Nonuniform Cosine Modulated Filter Banks,” IEEE Trans. Circuits Syst. II Analog Digit. Signal Process., 42(11)732–737. https://doi.org/10.1109/82.475253
Xie XM, Chen XY, Shi GM (2005) A simple design method of linear-phase nonuniform filter banks with integer decimation factors. Midwest Symp Circuits Syst 2005:724–727. https://doi.org/10.1109/MWSCAS.2005.1594203
B Keerthana, N Raju, R CV, R Anbazhagan, T hoon Kim, and F Mohammad, (2024) “Designing optimal prototype filters for maximally decimated Cosine Modulated filter banks with rapid convergence,” Heliyon 10(11)e31912. https://doi.org/10.1016/j.heliyon.2024.e31912
Yang SJ, Lee JH, Chieu BC (1998) Perfect-reconstruction filter banks having linear-phase fir filters with equiripple response. IEEE Trans Signal Process 46(12):3246–3255. https://doi.org/10.1109/78.735300
Bergen SWA (2008) A design method for cosine-modulated filter banks using weighted constrained-least-squares filters. Digit Signal Process 18(3):282–290. https://doi.org/10.1016/J.DSP.2007.04.010
Soni R, Jain A, Saxena R (2013) An optimized design of nonuniform filter bank using variable-combinational window function. AEU - Int J Electron Commun 67(7):595–601. https://doi.org/10.1016/J.AEUE.2013.01.003
Ogale J, Ashok S (2011) Cosine Modulated Non-Uniform Filter Banks. J Signal Inf Process 2:178–183. https://doi.org/10.4236/jsip.2011.23024
Kalathil S, Elias E (2015) Non-uniform cosine modulated filter banks using meta-heuristic algorithms in CSD space. J Adv Res 6(6):839–849. https://doi.org/10.1016/J.JARE.2014.06.008
Vaidyanathan PP (1992) Cosine-Modulated FIR Filter Banks Satisfying Perfect Reconstruction. IEEE Trans Signal Process 40(4):770–783. https://doi.org/10.1109/78.127951
Kumar A, Singh GK, Anurag S (2015) An optimized cosine-modulated nonuniform filter bank design for subband coding of ECG signal. J King Saud Univ - Eng Sci 27(2):158–169. https://doi.org/10.1016/J.JKSUES.2013.10.001
Kumar A, Singh GK, Anurag S (2013) Design of nearly perfect reconstructed non-uniform filter bank by constrained equiripple FIR technique. Appl Soft Comput 13(1):353–360. https://doi.org/10.1016/J.ASOC.2012.08.024
Sakthivel V, Elias E (2018) Low complexity reconfigurable channelizers using non-uniform filter banks. Comput Electr Eng 68:389–403. https://doi.org/10.1016/J.COMPELECENG.2018.04.015
Li J, Nguyen TQ, Tantaratana S (1997) A simple design method for near-perfect-reconstruction nonuniform filter banks. IEEE Trans Signal Process 45(8):2105–2109. https://doi.org/10.1109/78.611222
“An optimized design of Non-uniform filter bank using Blackman Window family | Request PDF.” Accessed: Oct. 11, 2022. [Online]. Available: https://www.researchgate.net/publication/235683862_An_optimized_design_of_Non-uniform_filter_bank_using_Blackman_Window_family
Elias E, Löwenborg P, Johansson H, Wanhammar L (2003) Tree-structured IIR/FIR uniform-band and octave-band filter banks with very low-complexity analysis or synthesis filters. Signal Process 83(9):1997–2009. https://doi.org/10.1016/S0165-1684(03)00131-2
Z Zijing and Y Yun, (2007) “A simple design method for nonuniform cosine modulated filter banks,” IEEE 2007 Int. Symp. Microwave, Antenna, Propag. EMC Technol. Wirel. Commun. MAPE, pp. 1052–1055. https://doi.org/10.1109/MAPE.2007.4393448
Salcedo-Sanz S, Cruz-Roldán F, Heneghan C, Yao X (2007) Evolutionary design of digital filters with application to subband coding and data transmission. IEEE Trans Signal Process 55(4):1193–1203. https://doi.org/10.1109/TSP.2006.888883
Jalaleddine SMS, Hutchens CG, Strattan RD, Coberly WA (1990) ECG data compression techniques–a unified approach. IEEE Trans Biomed Eng 37(4):329–343. https://doi.org/10.1109/10.52340
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no relevant conflicts of interest to disclose.
Ethical approval
This article does not contain any studies with human participants or animals performed by any authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Keerthana, B., Raju, N. Improvised method for analysis and synthesis of NUFB for Speech and ECG signal applications. Multimed Tools Appl 83, 86007–86024 (2024). https://doi.org/10.1007/s11042-024-20211-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11042-024-20211-0