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Active Noise Reduction by the Filtered xLMS Algorithm

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Paper presented at the Recent Trends in Electrical, Electronics and Communications Engineering Conference at ITM Universe in January 2014

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Active Noise Reduction by the Filtered xLMS Algorithm

  1. 1. Recent Trends in Electrical, Electronics and Communications Engineering Conference 2014 ITM Universe, Vadodara, Gujarat Active Noise Cancellation by the modified filtered xLMS algorithm with online secondary path modelling Author: Nirav Desai Asst. Professor, Department of Electronics and Communications Engg. ITM Universe, Vadodara (Affiliated to Gujarat Technological University) Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe
  2. 2. Active Noise Cancellation: Problem Statement and System Development Active Noise Cancellation: Problem Definition LMS approach to active noise cancellation System diagram for slow adaptation Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe
  3. 3. Classic Least Mean Square Algorithm 𝑒(𝑛) = 𝑑(𝑛) βˆ’ 𝑦(𝑛) … (1) 𝑦 𝑛 = π‘₯ 𝑛 βˆ— 𝑀 𝑛 … (2) 𝑦 𝑛 = 𝑦′ 𝑛 … (3) πΆπ‘œπ‘ π‘‘ π‘“π‘’π‘›π‘π‘‘π‘–π‘œπ‘› 𝐽 𝑛 = 𝐸 𝑒 𝑛 𝑒 𝑛 𝐽 𝑛 = 𝐸 𝑑 𝑛 βˆ’ 𝑦 𝑛 βˆ— 𝑑 𝑛 βˆ’ 𝑦 𝑛 𝑦 𝑛 = 𝑀 𝑛 βˆ— π‘₯ 𝑛 … 5 𝑀 𝑛 + 1 = 𝑀 𝑛 + πœ‡π‘₯ 𝑛 𝑒 𝑛 … 6 System identification using LMS Algorithm … (4) Design equations for LMS algorithm [2] Adaptive Filter Theory: Book by Simon Haykin Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe
  4. 4. Modified Least Mean Square Algorithm 𝑦 𝑛 = π‘Ž1 βˆ™ π‘₯ 𝑛 βˆ’ 1 + π‘Ž2 βˆ™ π‘₯ 𝑛 βˆ’ 2 + π‘Ž3 βˆ™ π‘₯ 𝑛 βˆ’ 3 … (7) 𝑑 𝑛 = π‘₯ 𝑛 … 8 𝑒 𝑛 = 𝑑 𝑛 βˆ’ 𝑦 𝑛 = π‘₯ 𝑛 βˆ’ π‘Ž1 βˆ™ π‘₯ 𝑛 βˆ’ 1 βˆ’ π‘Ž2 βˆ™ π‘₯ 𝑛 βˆ’ 2 βˆ’ π‘Ž3 βˆ™ π‘₯ 𝑛 βˆ’ 3 … (9) π‘₯ 𝑛 βˆ’ π‘Ž1 βˆ™ π‘₯ 𝑛 βˆ’ 1 βˆ’ π‘Ž2 βˆ™ π‘₯ 𝑛 βˆ’ 2 βˆ’ π‘Ž3 βˆ™ π‘₯ 𝑛 βˆ’ 3 βˆ™ 𝐸 𝑒 𝑛 βˆ™ 𝑒 𝑛 = 𝐸 … 10 π‘₯ 𝑛 βˆ’ π‘Ž1 βˆ™ π‘₯ 𝑛 βˆ’ 1 βˆ’ π‘Ž2 βˆ™ π‘₯ 𝑛 βˆ’ 2 βˆ’ π‘Ž3 βˆ™ π‘₯ 𝑛 βˆ’ 3 𝐸 𝑒 𝑛 2 = 𝜎 2 βˆ’ π‘Ž1𝑅 π‘₯π‘₯ βˆ’1 βˆ’ π‘Ž2𝑅 π‘₯π‘₯ βˆ’2 βˆ’ π‘Ž3𝑅 π‘₯π‘₯ βˆ’3 βˆ’ π‘Ž1𝑅 π‘₯π‘₯ βˆ’1 + π‘Ž12 𝑅 π‘₯π‘₯ 0 + π‘₯ π‘Ž1π‘Ž2𝑅 π‘₯π‘₯ βˆ’1 + π‘Ž1π‘Ž3𝑅 π‘₯π‘₯ βˆ’2 + π‘Ž2π‘Ž3𝑅 π‘₯π‘₯ βˆ’1 + π‘Ž22 𝑅 π‘₯π‘₯ 0 + π‘Ž1π‘Ž2𝑅 π‘₯π‘₯ βˆ’1 βˆ’ π‘Ž2𝑅 π‘₯π‘₯ βˆ’2 βˆ’ π‘Ž3𝑅 π‘₯π‘₯ 3 + π‘Ž1π‘Ž3𝑅 π‘₯π‘₯ 2 + π‘Ž2π‘Ž3𝑅 π‘₯π‘₯ 1 + π‘Ž32 𝑅 π‘₯π‘₯ 0 … 11 πœ•πΈ 𝑒 𝑛 2 πœ•π‘Ž1 πœ•πΈ 𝑒 𝑛 2 πœ•π‘Ž2 πœ•πΈ 𝑒 𝑛 2 πœ•π‘Ž3 = 2π‘Ž2 βˆ’ 2 𝑅 π‘₯π‘₯ βˆ’1 + 2π‘Ž1𝑅 π‘₯π‘₯ 0 + 2π‘Ž3𝑅 π‘₯π‘₯ 2 … 12 = 2π‘Ž2𝑅 π‘₯π‘₯ 0 + 2π‘Ž1 + 2π‘Ž3 𝑅 π‘₯π‘₯ βˆ’1 βˆ’ 2𝑅 π‘₯π‘₯ βˆ’2 … 13 = 2π‘Ž3𝑅 π‘₯π‘₯ 0 + 2π‘Ž2𝑅 π‘₯π‘₯ 1 + 2π‘Ž1𝑅 π‘₯π‘₯ 2 βˆ’ 2𝑅 π‘₯π‘₯ 3 … 14 Tap weight updates: βˆ’π›»π‘Ž1 = βˆ’2𝑅 π‘₯π‘₯ 0 π‘Ž1 βˆ’ 𝑅 π‘₯π‘₯ 1 2π‘Ž2 βˆ’ 2 π‘Ž1 βˆ’ 2𝑅 π‘₯π‘₯ 2 π‘Ž3 … (15) βˆ’π›»π‘Ž2 = βˆ’2𝑅 π‘₯π‘₯ 0 π‘Ž2 βˆ’ 𝑅 π‘₯π‘₯ 1 2π‘Ž3 + 2π‘Ž1 + 2𝑅 π‘₯π‘₯ 2 π‘Ž2 … (16) βˆ’π›»π‘Ž3 = βˆ’2𝑅 π‘₯π‘₯ 0 π‘Ž3 βˆ’ 𝑅 π‘₯π‘₯ 1 2π‘Ž2) βˆ’ 𝑅 π‘₯π‘₯ (2)(2π‘Ž1 + 2𝑅 π‘₯π‘₯ 3 π‘Ž3 … (17) Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe
  5. 5. Modified filtered x-LMS with Online Secondary Path Modelling FXLMS without modifications Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe
  6. 6. Code Snippet for simulation on SCILAB Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe
  7. 7. Extraction of channel statistics from available data Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe
  8. 8. Estimation of channel model in 1st, 2nd and 3rd order Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe
  9. 9. Estimation of noise signal by the FXLMS algorithm Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe
  10. 10. Adaptive step size used by modified LMS algorithm Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe
  11. 11. Mean square estimation error of noise by algorithm Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe
  12. 12. Mean square estimation error w/o modification of FXLMS algorithm Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe
  13. 13. Hardware setup for test of noise cancelling algorithm Condensor Mic 3mH inductor Second order low pass filter with 10uF Ceramic capacitors Arduino UNO With Atmel ATMEGA Microcontroller Having 8 bit PWM audio out Need better hardware such as a Texas Instruments DSP or ARM Cortex M3/M4 processor Add output drivers, use active filters. Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe
  14. 14. REFERENCES: [1] Active Noise Control: A Tutorial Review Sen M. Kuo and Dennis R. Morgan, Senior Member IEEE PROCEEDINGS OF THE IEEE, VOL. 87, NO. 6, JUNE 1999 [2] Adaptive Filter Theory by Simon Haykin [3] Active Noise Cancellation System using DSP Processor G.U.Priyanga, T.Sangeetha, P.Saranya, Mr.B.Prasad International Journal of Scientific & Engineering Research, Volume 4, Issue 4, April-2013
  15. 15. Thank you for your attention. Questions? Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe

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