Performance analysis of adaptive noise canceller for an ecg signal

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In numerous applications of signal processing, communications and biomedical we are faced with the necessity to remove noise and distortion from the signals. Adaptive filtering is one of the most important areas in digital signal processing to remove background noise and distortion. In last few years various adaptive algorithms are developed for noise cancellation. In this paper we present an implementation of LMS (Least Mean Square), NLMS (Normalized Least Mean Square) and RLS (Recursive Least Square) algorithms on MATLAB platform with the intention to compare their performance in noise cancellation. We simulate the adaptive filter in MATLAB with a noisy ECG signal and analyze the performance of algorithms in terms of MSE (Mean Squared Error), SNR Improvement, computational complexity and stability. The obtained results shows that RLS has the best performance but at the cost of large computational complexity and memory requirement.

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Performance analysis of adaptive noise canceller for an ecg signal

  1. 1. “Performance analysis of AdaptiveNoise Canceller for an ECG signal” Raj Kumar Thenua Anand Engineering College, Agra, U.P., India E-mail:rkthenua@gmail.com Web: www.rkthenua.in
  2. 2. Outline Need of Noise Cancellation Adaptive Filters Approaches to Adaptive Filtering MATLAB Simulation Performance Comparison Conclusions References 2
  3. 3. Need of Noise Cancellation In the process of transmission of information, noise gets added to the signal from the surroundings automatically . It reduces the perceived quality or intelligibility of the signal. The effective removal or reduction of noise is an active area of research . In a general sense, noise cancellation has applications in various fields such as channel equalization, radar signal processing, pattern analysis, data forecasting, biomedical signal processing etc. In this work a MATLAB simulation is carried out for de- noising a biomedical ECG signal in a noisy environment. 3
  4. 4. Adaptive Filters In order to design a filter, a priori knowledge of the desired response is required. When such knowledge is not available, due to the changing nature of the filter’s requirements. It is impossible to design a standard digital filter. In such situations, adaptive filters are desirable. Adaptive filters continuously change their impulse response in order to satisfy the given condition. Adaptive filters are capable of learning from the statistics of current conditions. Change their coefficients in order to achieve a certain goal. 4
  5. 5. Real Life Examples of Adaptive Filtering:Example-1: A good example to illustrate the principles of adaptive noise cancelling is the noise removal from the pilot’s microphone in the airplane. Due to the high environmental noise produced by the airplane engines, the pilot’s voice in the microphone is distorted with a high amount of noise, and can be very difficult to understand. In order to overcome the problem, an adaptive filter can be used. 5
  6. 6. Example-2: To measure the ECG of a pregnant lady and her baby which is to be born, measurement of mother’s ECG is simple but it is very difficult for the baby, here the concept of adaptive filtering is used. The mother’s heart sound acts as a noise signal and we have to cancel that noise using various adaptive algorithms. 6
  7. 7. Adaptive Noise Canceller Fig. 1 Adaptive Noise Canceller 7
  8. 8. Approaches to adaptive filtering Adaptive Filtering Stochastic Gradient Approach Least Square Estimation ( Least Mean Square Algorithms) ( Recursive Least Square algorithm) LMS NLMS RLS TVLMS FTRLS VSSNLMS 8
  9. 9. LMS Algorithm• Filter weights are updated by the following formula for each iteration: Here x(n) is the input vector of time delayed input values, w(n) represents the coefficients of the adaptive FIR filter tap weight vector at time n.• μ is known as the step size,• If μ is too small ;converge on the optimal solution will be too long;• if μ is too large; the adaptive filter becomes unstable and its output diverges. 9
  10. 10. NLMS Algorithm• The step size is normalized by the input signal power.• The NLMS is always the favorable choice of algorithm for fast convergence speed and for non-stationary input.• α: NLMS adaption constant, which optimize the convergence rate of algorithm.• 0<α<2 (practically <1)• c : constant term for normalization 10
  11. 11. RLS Algorithm RLS algorithms are known for excellent performance when working in time varying environments. cost of an increased computational complexity and some stability problems. Filter tap weight vector is updated using equation wn w T n 1 k n en 1 n intermediate gain vector k n un / xT n u n The filter output is calculated using the filter tap weights from the previous iteration and the current input vector. yn 1 n w T n 1 x n en 1 n d n yn 1 n 11
  12. 12. MATLAB Simulation The adaptive noise canceller is implemented in MATLAB for three algorithms; LMS, NLMS and RLS [7]. In the simulation the reference input signal x(n) is a white Gaussian noise of power 1-dB generated using randn function in MATLAB, and source signal s(n) is a clean amplified ECG signal recorded with 12-lead configuration [6]. The desired signal d(n) ,obtained by adding a delayed version of x(n) into clean signal s(n), d(n) = s(n) + x1(n). 12
  13. 13. Results Fig. 2 (a) Clean ECG signal s(n);(b) Noise signal x(n);(c) desired signal d(n) 13
  14. 14. Results Contd... Fig.3. MATLAB simulation for LMS algorithm; N=19, step size=0.009 Fig.4. MATLAB simulation for NLMS algorithm; N=19, c=0.001 , alpha= 0.07 14
  15. 15. Results Contd... Fig.5. MATLAB simulation for RLS algorithm; N=19If we investigate the filtered output of all algorithms, LMSadopt the approximate correct output in 750 samples,NLMS adopt in 600 samples and RLS adopt in 250samples. This shows that RLS has fast learning rate. 15
  16. 16. Results Analysis Table. 1 Performance Comparison of adaptive algorithms S.N. Algorithm MSE Complexity Stability 1. LMS 1.5×10-2 2N+1 Highly Stable 2. NLMS 9.0×10-3 3N+1 Stable 3. RLS 6.2×10-3 4N2 Less Stable 16
  17. 17. Results Analysis Table. 2 Performance Comparison of adaptive algorithms S.N. Algorithm SNR Pre SNR Post SNR dB dB Improved dB 1. LMS 0.89 7.04 6.15 2. NLMS 0.89 9.26 8.37 3. RLS 0.89 10.87 9.98 17
  18. 18. Conclusions The main objective of this paper was to implement an adaptive noise canceller for de-noising an ECG signal and test the performance of the system for various adaptive algorithms. When input signal is non-stationary in nature, the RLS algorithm proved to have the highest convergence speed, less MSE, and higher SNR Improvement but at the cost of large computational complexity and memory requirement. The NLMS algorithm changes the step-size according to the energy of input signals hence it is suitable for both stationary as well as non-stationary environment and its performance lies between LMS and RLS. Hence it provides a trade-off in convergence speed and computational complexity. The implementation of algorithms was successfully achieved, with results that have a really good response. 18
  19. 19. REFERENCES[1] Bernard Widrow, John R. Glover, John M. Mccool, John Kaunitz, Charles S. Williams, Robert H. Hean, James R. Zeidler, Eugene Dong, Jr. and Robert C. Goodlin, “Adaptive Noise Cancelling: Principles and Applications”, Proceedings of the IEEE, 1975, Vol.63 , No. 12 , Page(s): 1692 – 1716.[2] J. Benesty, et. al. , “Adaptive Filtering Algorithms for Stereophonic Acoustic Echo Cancellation”, International Conference on Acoustics, Speech, and Signal Processing, 1995, vol.5, Page(s): 3099 – 3102.[3] Simon Haykin, “Adaptive Filter Theory”, Prentice Hall, 4th edition.[4] Paulo S.R. Diniz, “Adaptive Filtering: Algorithms and Practical Implemetations” ,ISBN 978-0-387-31274-3, Kluwer Academic Publisher © 2008 Springer Science+Business Media, LLC, pp.77-195. 19
  20. 20. REFERENCES[5] Abhishek Tandon, M. Omair Ahmad, “An efficient, low- complexity, normalized LMS algorithm for echo cancellation” The 2nd Annual IEEE Northeast Workshop on Circuits and Systems, 2004. NEWCAS 2004, Page(s): 161 – 164.[6] Ch. Renumadhavi, Dr. S.Madhava Kumar, Dr. A. G. Ananth, Nirupama Srinivasan, “A New Approach for Evaluating SNR of ECG Signals and Its Implementation”, Proceedings of the 6th WSEAS International Conference on Simulation, Modelling and Optimization, Lisbon, Portugal, September 22-24, 2006.[7] Ying He, et. al. “The Applications and Simulation of Adaptive Filter in Noise Canceling”, 2008 International Conference on Computer Science and Software Engineering, 2008, Vol.4, Page(s): 1 – 4.[8] Cristina Gabriela SĂRĂCIN, Marin SĂRĂCIN, Mihai DASCĂLU, Ana-Maria LEPAR, “Echo Cancellation Using The LMS Algorithm”, U.P.B. Sci. Bull., Series C, Vol. 71, No. 4, 2009. 20

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