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

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. 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. Classic Least Mean Square Algorithm
𝑒(𝑛) = 𝑑(𝑛) − 𝑦(𝑛) … (1)
𝑦 𝑛 = 𝑥 𝑛 ∗ 𝑤 𝑛 … (2)
𝑦 𝑛 = 𝑦′ 𝑛 …
(3)
𝐶𝑜𝑠𝑡 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝐽 𝑛 = 𝐸 𝑒 𝑛 𝑒 𝑛
𝐽 𝑛 = 𝐸 𝑑 𝑛 − 𝑦 𝑛 ∗ 𝑑 𝑛 − 𝑦 𝑛
𝑦 𝑛 = 𝑤 𝑛 ∗ 𝑥 𝑛 … 5
𝑤 𝑛 + 1 = 𝑤 𝑛 + 𝜇𝑥 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. Modified Least Mean Square Algorithm
𝑦 𝑛 = 𝑎1 ∙ 𝑥 𝑛 − 1 + 𝑎2 ∙ 𝑥 𝑛 − 2 + 𝑎3 ∙ 𝑥 𝑛 − 3 … (7)
𝑑 𝑛 = 𝑥 𝑛 … 8
𝑒 𝑛 = 𝑑 𝑛 − 𝑦 𝑛 = 𝑥 𝑛 − 𝑎1 ∙ 𝑥 𝑛 − 1 − 𝑎2 ∙ 𝑥 𝑛 − 2 − 𝑎3 ∙ 𝑥 𝑛 − 3 … (9)
𝑥 𝑛 − 𝑎1 ∙ 𝑥 𝑛 − 1 − 𝑎2 ∙ 𝑥 𝑛 − 2 − 𝑎3 ∙ 𝑥 𝑛 − 3 ∙
𝐸 𝑒 𝑛 ∙ 𝑒 𝑛 = 𝐸
… 10
𝑥 𝑛 − 𝑎1 ∙ 𝑥 𝑛 − 1 − 𝑎2 ∙ 𝑥 𝑛 − 2 − 𝑎3 ∙ 𝑥 𝑛 − 3
𝐸 𝑒 𝑛 2 = 𝜎 2 − 𝑎1𝑅 𝑥𝑥 −1 − 𝑎2𝑅 𝑥𝑥 −2 − 𝑎3𝑅 𝑥𝑥 −3 − 𝑎1𝑅 𝑥𝑥 −1 + 𝑎12 𝑅 𝑥𝑥 0 +
𝑥
𝑎1𝑎2𝑅 𝑥𝑥 −1 + 𝑎1𝑎3𝑅 𝑥𝑥 −2 + 𝑎2𝑎3𝑅 𝑥𝑥 −1 + 𝑎22 𝑅 𝑥𝑥 0 + 𝑎1𝑎2𝑅 𝑥𝑥 −1 −
𝑎2𝑅 𝑥𝑥 −2 − 𝑎3𝑅 𝑥𝑥 3 + 𝑎1𝑎3𝑅 𝑥𝑥 2 + 𝑎2𝑎3𝑅 𝑥𝑥 1 + 𝑎32 𝑅 𝑥𝑥 0 … 11
𝜕𝐸 𝑒 𝑛 2
𝜕𝑎1
𝜕𝐸 𝑒 𝑛 2
𝜕𝑎2
𝜕𝐸 𝑒 𝑛 2
𝜕𝑎3
= 2𝑎2 − 2 𝑅 𝑥𝑥 −1 + 2𝑎1𝑅 𝑥𝑥 0 + 2𝑎3𝑅 𝑥𝑥 2 … 12
= 2𝑎2𝑅 𝑥𝑥 0 + 2𝑎1 + 2𝑎3 𝑅 𝑥𝑥 −1 − 2𝑅 𝑥𝑥 −2 … 13
= 2𝑎3𝑅 𝑥𝑥 0 + 2𝑎2𝑅 𝑥𝑥 1 + 2𝑎1𝑅 𝑥𝑥 2 − 2𝑅 𝑥𝑥 3 … 14
Tap weight updates:
−𝛻𝑎1 = −2𝑅 𝑥𝑥 0 𝑎1 − 𝑅 𝑥𝑥 1 2𝑎2 − 2 𝑎1 − 2𝑅 𝑥𝑥 2 𝑎3 … (15)
−𝛻𝑎2 = −2𝑅 𝑥𝑥 0 𝑎2 − 𝑅 𝑥𝑥 1 2𝑎3 + 2𝑎1 + 2𝑅 𝑥𝑥 2 𝑎2 … (16)
−𝛻𝑎3 = −2𝑅 𝑥𝑥 0 𝑎3 − 𝑅 𝑥𝑥 1 2𝑎2) − 𝑅 𝑥𝑥 (2)(2𝑎1 + 2𝑅 𝑥𝑥 3 𝑎3 … (17)
Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe

5. Modified filtered x-LMS with
Online Secondary Path Modelling
FXLMS without modifications
Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe

6. Code Snippet for simulation on SCILAB
Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe

7. Extraction of channel statistics from available data
Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe

8. Estimation of channel model in 1st, 2nd and 3rd order
Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe

9. Estimation of noise signal by the FXLMS algorithm
Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe

10. Adaptive step size used by modified LMS algorithm
Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe

11. Mean square estimation error of noise by algorithm
Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe

12. Mean square estimation error w/o modification of
FXLMS algorithm
Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe

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. 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. Thank you for your attention.
Questions?
Nirav Desai, Asst. Professor, Dept. of ECE, ITM Universe