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In this paper, new algorithms robust to a mix of Gaussian and impulsive noises that approximate an unknown sparse impulse response of an LTI system are proposed. They are using the sigmoid cost function and based on the Least-Mean Mixed-Norm (LMMN) adaptive algorithm. It is shown by simulations that the proposed sigmoid LMMN (SLMMN) algorithms that exploit sparsity-enforcing penalties achieve superior performance to other competing algorithms in the sparse system identification context.

Adaptive filters are extensively used in the identification of an unknown system. Unlike several gradient-search based adaptive filtering techniques, the Lyapunov Theory-based Adaptive Filter offers improved convergence and stability. When the system is described by a sparse model, the performance of Lyapunov Adaptive (LA) filter is degraded since it fails to exploit the system sparsity. In this paper, the Zero-Attracting Lyapunov Adaptation algorithm (ZA-LA), the Reweighted Zero-Attracting Lyapunov Adaptation algorithm (RZA-LA) and an affine combination scheme of the LA and proposed ZA-LA filters are proposed. The ZA-LA algorithm is based on ℓ1-norm relaxation while the RZA-LA algorithm uses a log-sum penalty to accelerate convergence when identifying sparse systems. It is shown by simulations that the proposed algorithms can achieve better convergence than the existing LMS/LA filter for a sparse system, while the affine combination scheme is robust in identifying systems with variable sparsity.

Low complexity Normalized Least Mean Square (NLMS) adaptive algorithm is widely used in the adaptive system identification applications. To exploit the sparse impulse response of the system, different sparse penalties are introduced into the error function of the NLMS algorithm. Reweighted Zero Attracting-NLMS (RZA-NLMS) algorithm based on 11-norm relaxation offers improved performance in identifying the system with sparse echo path but when the system is non-sparse, NLMS algorithm dominates the sparse adaptive algorithm. In order to identify the system with varying sparseness, a new strategy is required. In this paper, we propose an affine combination of RZA-NLMS and NLMS filters used for system identification with variable sparsity. The robust performance of our proposed approach has been verified from the MATLAB simulations.

Speech enhancement is a long standing problem with numerous applications like teleconferencing, VoIP, hearing aids and speech recognition. The motivation behind this research work is to obtain a clean speech signal of higher quality by applying the optimal noise cancellation technique. Real-time adaptive filtering algorithms seem to be the best candidate among all categories of the speech enhancement methods. In this paper, we propose a speech enhancement method based on Recursive Least Squares (RLS) adaptive filter of speech signals. Experiments were performed on noisy data which was prepared by adding AWGN, Babble and Pink noise to clean speech samples at -5dB, 0dB, 5dB and 10dB SNR levels. We then compare the noise cancellation performance of proposed RLS algorithm with existing NLMS algorithm in terms of Mean Squared Error (MSE), Signal to Noise ratio (SNR) and SNR Loss. Based on the performance evaluation, the proposed RLS algorithm was found to be a better optimal noise cancellation technique for speech signals., {"references":["P. Krishnamoorthy and S.R. Mahadeva Prasanna, \"Temporal and\nSpectral Processing Methods for Processing of Degraded Speech: A\nReview,\" IETE Technical Review, Vol. 26, No. 2, March 2009.","Jingdong C., Jacob B. and Arden Huang., \"On the optimal linear\nfiltering techniques for noise reduction,\" Speech Communications, Vol.\n49, No. 4, April 2007, pp. 305-316.","Jan Vanus and Vitezslav Styskala, \"Application of optimal settings of\nthe LMS adaptive filter for speech signal processing,\" Proceedings of\nthe 2010 International multiconference on Computer Science and\nInformation Technology, October 2010, pp.767-774.","Paulo S.R. Diniz, Adaptive Filtering: Algorithms and Practical\nImplementation, Springer, 2013.","Raj Kumar Thenua and S.K. Agarwal, \"Simulation and performance\nanalysis of adaptive filter in noise cancellation,\" International Journal of\nEngineering Science and Technology, Vol. 2, No. 9, 2010, pp. 4373-\n4378.","Simon Haykin, Adaptive Filter Theory, Prentice- Hall, 2002.","Emmanuel Ifeachor C., Jervis Barrie W., Digital Signal Processing – A\npractical approach, Pearson Education, 2004.","M. Turki-Hadj Alouane and M. Jaídane-Saídane, \"A new nonstationary\nLMS algorithm for tracking Markovian time varying systems,\" Signal\nProcessing, Volume 86, No. 1, January 2006 pp. 50-70.","A.H. Sayed, Fundamentals of Adaptive Filtering, Wiley, 2003. [10] J. H. Husoy and M. S. E. Abadi, \"A comparative study of some\nsimplified RLS type algorithm,\" Proceedings of International\nSymposium on control, Communications and Signal Processing, March\n2004, pp.705-708.\n[11] Komal R. Borisagar and Dr. G.R.Kulkarni, \"Simulation and\nComparative Analysis of LMS and RLS Algorithms Using Real Time\nSpeech Input Signal,\" Global Journal of Researches in Engineering,\nVol. 10, No. 5, October 2010, pp. 44-47.\n[12] Jianfen Maa and Philipos C. Loizou, \"SNR loss: A new objective\nmeasure for predicting the intelligibility of noise-suppressed speech,\"\nSpeech Communication, Vol. 53, No. 3, March 2011, pp. 340–354."]}