Sparse FIR Filter Design using Double Generalized Orthogonal Matching Pursuit (DGOMP)
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Published:
Aug 12, 2024
Keywords:
Sparsity, Filter, Fourier Transform, Finite Impulse Response Filter, Mean Square, Error, Correlation
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Abstract
In this paper, sparse FIR filter was designed using Double Generalized Orthogonal Matching Pursuit (DGOMP) to reduce memory usage and increasing the speed thereby decreasing computational complexity of the algorithm. Mathematical models were formulated and simulations were conducted to validate the performance of the proposed method. The performance was compared with BOMP and Conventional FIR filter. The results showed that the DGOMP method achieved higher sparsity and a better approximation of an ideal filter. Additionally, the designed sparse FIR filters using DGOMP showed better performance in terms of time of execution when the signal lengths keep increasing, giving a 10% faster execution time when compared to BOMP. The passband and stopband attenuation, as well as ripple values were better, offering the flexibility of parameter adjustment. The results showed that DGOMP is a promising approach for designing sparse FIR filters.
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How to Cite
[1]
S. F. Kolawole, F. M. Isah, N. A. Musa, and A. A. Ahmad, “Sparse FIR Filter Design using Double Generalized Orthogonal Matching Pursuit (DGOMP)”, AJERD, vol. 7, no. 2, pp. 115-126, Aug. 2024.
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References
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[19] Li, H., Ying, H., & Li, E. (2022). Graph-Based Convex Optimization for Sparse FIR Filter Design. IEEE Transactions on Circuits and Systems I: Regular Papers, 69(4), 1525-1537. doi: 10.1109/TCSI.2022.3162183.
[20] Yu, L., & Zhao, J. (2019). Hybrid Optimization Method of Sparse FIR DFEs Based on Reweighted ℓ1-Norm Minimization and Greedy Algorithms. Electronics Letters, 55(8), 491-493. doi: 10.1049/el.2018.7438.
[21] Kwan,H.K., Liang, J . & Jiang , A . (2018). Sparse Linear Phase FIR Filter Design using Iterative CSA. In 2018 IEEE 23rd International Conference on Digital Signal Processing (DSP), 1-4. doi:10.1109/ICDSP.2018.8631659.
[22] Li, H., Ying, H. & Liu, X. Binary generalized orthogonal matching pursuit. Japan J. Indust. Appl. Math. 41(1), 1–12 (2024). https://doi.org/10.1007/s13160-023-00585-8
[23] Chen,.& Lou ,X. (2022). Design of Linear-Phase Sparse FIR Filter Using Iterative Root Method and Improved LSQR Algorithm. IEEE Transactions n Circuits and Systems I :Regular Papers, 69(10), 3586–3598.doi:10.1109/TCSI.2022.3146438.
[24] Chen, W., Huang, M., & Lou, X. (2019). Sparse FIR Filter Design Based on Cascaded Compensation Structure. 2019 IEEE International Symposium on Circuits and Systems (ISCAS). 19(6) 1-5. doi:10.1109/iscas.2019.8702703.
[2] Srivastava, S., Dwivedi, A.K., & Nagaria, D. (2020). Low Complexity FIR Filter Design using Biogeography Optimization Algorithm and its Improved Version. In 2020 IEEE Students Conference on Engineering & Systems (SCES), 1-5. doi: 10.1109/SCES50439.2020.9236706.
[3] Jayaweera, A.L., Pakiyarajah, D., & Edussooriya, C.U.S. (2022). Minimax Design of M-D Sparse FIR Filters With Arbitrary Frequency Response Using SOCP. IEEE Transactions on Circuits and Systems II: Express Briefs, 69(5), 2403-2407. doi: 10.1109/TCSII.2022.3160400.
[4] Z. Bai, "Sparse Bayesian learning for sparse signal recovery using ℓ₁/₂-norm," Appl. Acoustics, vol. 207, pp. 109340, 2023, doi: 10.1016/j.apacoust.2023.109340.
[5] Xi, X., & Lou, Y. (2021). Sparse FIR Filter Design With k-Max Sparsity and Peak Error Constraints." IEEE Transactions on Circuits and Systems II: Express Briefs, 68(4), 1497-1501. doi: 10.1109/TCSII.2020.3027704.
[6] Li, Y., Zhao, J., Xu, W., & Sun, G. (2022). A Low Computational Complexity Scheme for Designing Linear Phase Sparse FIR Filters. Circuits, Systems, and Signal Processing, 41(1), 1-13. doi: 10.1007/s00034-021-01836-0.
[7] Kwan, H.K., Liang, J., & Jiang, A. (2018). Sparse FIR Filter Design using Iterative MOCSA. In 2018 IEEE 61st International Midwest Symposium on Circuits and Systems (MWSCAS) 952-955. doi: 10.1109/MWSCAS.2018.8623954.
[8] Nakamoto, M., Itani, T., & Konishi, K. (2018). Optimal Least-Squares Design of Sparse FIR Filters for Big-Data Signal Processing. In 2018 IEEE 23rd International Conference on Digital Signal Processing (DSP) 1-5. doi: 10.1109/ICDSP.2018.8631598.
[9] Yang, Y., Zhu, W.-P., & Yan, J. (2017). Minimax design of orthogonal filter banks with sparse coefficients. In 2017 IEEE 30th Canadian Conference on Electrical and Computer Engineering (CCECE) 1-4. doi: 10.1109/CCECE.2017.7946804.
[10] Bellotti, M.J., & Vucic, M. (2019). Design of Nonlinear-Phase FIR-Filters Based on Signomial Programming. In 2019 11th International Symposium on Image and Signal Processing and Analysis (ISPA), 26(1) 141-146). doi: 10.1109/ISPA.2019.8868506.
[11] Yadav, S., Kumar, M., Yadav, R., & Kumar, A. (2020). Efficient Design of Sparse FIR Digital Filter. In 2020 2nd International Conference on Advances in Computing, Communication Control and Networking (ICACCCN). 647-651. doi: 10.1109/ICACCCN51052.2020.9362902.
[12] Srivastava, S., Dwivedi, A., & Nagaria, D. (2019). Sparse Finite Impulse Response Low Pass Filter Design using Improved Firefly Algorithm. Journal of Surface Engineered Materials and Advanced Technology, 9, 2061-2066. doi: 10.35940/ijeat.A9568.109119.
[13] Brajevic, I., & Stanimirovic, P. (2018). An improved chaotic firefly algorithm for global numerical optimization. International Journal of Computational Intelligence Systems, 12(1), 131-148. doi: 10.2991/ijcis.2018.25905187.
[14] Wang, H., Zhao, Z., & Zhao, L. (2020). Matrix Decomposition Based Low-Complexity FIR Filter: Further Results. IEEE Transactions on Circuits and Systems I: Regular Papers, 67(2), 672–685.
[15] Maja, J. B. (2023). Design of sparse systems based on optimization methods [Review of Design of sparse systems based on optimization methods] 1–128.downloaded from : https://urn.nsk.hr/urn:nbn:hr:168:097909.
[16] Chen, W, M. Huang X. Lou. (2018). Sparse FIR Filter Design Based on Interpolation Technique. In 2018 IEEE 23rd International Conference on Digital Signal Processing (DSP) 1-5. doi: 10.1109/ICDSP.2018.8631685.
[17] Premaratne, S. U., Edussooriya, C. U. S., Wijenayake, C., Bruton, L. T., & Agathoklis, P. (2018). A 4-D Sparse FIR Hyperfan Filter for Volumetric Refocusing of Light Fields by Hard Thresholding. In 2018 IEEE 23rd International Conference on Digital Signal Processing (DSP). doi: 10.1109/ICDSP.2018.8631601.
[18] Wijesekara, R.T., Edussooriya,C.U.S., Bruton, L.T &Agathoklis, P. (2019). A 3-D Sparse FIR Frustum Filter for Enhancing Broadband Plane Waves. IEEE Transactions on Circuits and Systems II: Express Briefs, 66(3), 497-501. doi: 10.1109/TCSII.2018.2856848.
[19] Li, H., Ying, H., & Li, E. (2022). Graph-Based Convex Optimization for Sparse FIR Filter Design. IEEE Transactions on Circuits and Systems I: Regular Papers, 69(4), 1525-1537. doi: 10.1109/TCSI.2022.3162183.
[20] Yu, L., & Zhao, J. (2019). Hybrid Optimization Method of Sparse FIR DFEs Based on Reweighted ℓ1-Norm Minimization and Greedy Algorithms. Electronics Letters, 55(8), 491-493. doi: 10.1049/el.2018.7438.
[21] Kwan,H.K., Liang, J . & Jiang , A . (2018). Sparse Linear Phase FIR Filter Design using Iterative CSA. In 2018 IEEE 23rd International Conference on Digital Signal Processing (DSP), 1-4. doi:10.1109/ICDSP.2018.8631659.
[22] Li, H., Ying, H. & Liu, X. Binary generalized orthogonal matching pursuit. Japan J. Indust. Appl. Math. 41(1), 1–12 (2024). https://doi.org/10.1007/s13160-023-00585-8
[23] Chen,.& Lou ,X. (2022). Design of Linear-Phase Sparse FIR Filter Using Iterative Root Method and Improved LSQR Algorithm. IEEE Transactions n Circuits and Systems I :Regular Papers, 69(10), 3586–3598.doi:10.1109/TCSI.2022.3146438.
[24] Chen, W., Huang, M., & Lou, X. (2019). Sparse FIR Filter Design Based on Cascaded Compensation Structure. 2019 IEEE International Symposium on Circuits and Systems (ISCAS). 19(6) 1-5. doi:10.1109/iscas.2019.8702703.