Comparison between Recursive Least Squares and Optimal Design Methods for Audio Enhancement

  • Teimour Tajdari Velayat University
Keywords: Adaptive filtering, Error, FIR filter, Noise, Optimal design, RLS filter


This study examines and compares the application of the optimal design method and the recursive least squares (RLS) method to improve the quality of the audio signal in noisy environments. Noise can be incorporated into audio signals through many sources, including amplification systems and electronic switches, which cause loss of signal information or affect the quality of the audio signal. RLS is an adaptive filtering procedure used to design a system that recursively minimizes the noise amplitude of a contaminated signal by comparing the filter output with a desired signal using new incoming signal samples. The optimal design is an FIR filter design technique that has been used to cut parts of the corrupted signal to improve the signal-to-noise ratio. In this study, samples of audio signals contaminated by white noise were used. The noise reduction results show that the RLS approach has vastly improved the quality of the signals. FIR filters, by contrast, can partially improve signal quality. The functionality of the RLS method depended highly on the precision of the measured noise signal. The FIR filter has shown much less signal improvement than the RLS method, but FIR filters are very practical when noise cannot be measured.


[1] J. Gnitecki, Z. Moussavi, and H. Pasterkamp, "Recursive least squares adaptive noise cancellation filtering for heart sound reduction in lung sounds recordings," in Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat. No.03CH37439), 2003, vol. 3, pp. 2416-2419 Vol.3.
[2] G. Lu et al., "Removing ECG noise from surface EMG signals using adaptive filtering," Neuroscience Letters, vol. 462, no. 1, pp. 14-19, 2009/09/18/ 2009.
[3] C. Stanciu, J. Benesty, C. Paleologu, T. Gänsler, and S. Ciochină, "A widely linear model for stereophonic acoustic echo cancellation," Signal Processing, vol. 93, no. 2, pp. 511-516, 2013/02/01/ 2013.
[4] A. Mirza, S. M. Kabir, S. Ayub, and S. A. sheikh, "Impulsive Noise Cancellation of ECG signal based on SSRLS," Procedia Computer Science, vol. 62, pp. 196-202, 2015/01/01/ 2015.
[5] R. Martinek, J. Rzidky, R. Jaros, P. Bilik, and M. Ladrova, "Least Mean Squares and Recursive Least Squares Algorithms for Total Harmonic Distortion Reduction Using Shunt Active Power Filter Control," Energies, vol. 12, no. 8, p. 1545, 2019.
[6] A. V. Oppenheim and R. W. Schafer, Discrete - Time Signal Processing, 3rd ed. United State: Pearson, 2014.
[7] A. Ambardar, Digital Signal Processing - A Modern Introduction, 1st ed. CL Engineering, 2006, p. 608.
[8] K. P. S. Rana, V. Kumar, and S. S. Nair, "Efficient FIR filter designs using constrained genetic algorithms based optimization," in 2016 2nd International Conference on Communication Control and Intelligent Systems (CCIS), 2016, pp. 131-135.
[9] H. K. Kwan and J. Liang, "Minimax design of linear phase FIR filters using cuckoo search algorithm," in 2016 8th International Conference on Wireless Communications & Signal Processing (WCSP), 2016, pp. 1-4.
[10] D. A. Alwahab, D. R. Zaghar, and S. Laki, "FIR Filter Design Based Neural Network," in 2018 11th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP), 2018, pp. 1-4.
[11] T. Kailath, Lectures on Wiener and Kalman Filtering. International Centre for Mechanical Sciences (Courses and Lectures): Springer, Vienna, 1981.
[12] L. Tan and J. Jiang, Digital Signal Processing Fundamentals and Applications, 2nd ed. USA: Academic Press, 2013, p. 896.
[13] S. Haykin, Adaptive Filter Theory, 3rd ed. United State: Pearson, 2013.
[14] Z. He, J. Zhang, and Z. Yao, "Determining the optimal coefficients of the explicit finite-difference scheme using the Remez exchange algorithm " GEOPHYSICS, vol. 84, no. 3, pp. S137-S147, May 2019.
How to Cite
Tajdari, T. (2020). Comparison between Recursive Least Squares and Optimal Design Methods for Audio Enhancement. Majlesi Journal of Telecommunication Devices, 9(3). Retrieved from