1. Study on the Use of Error Term in Parallel- form Narrowband Feedback Active Noise Control Systems Jianjun HE, Woon-Seng Gan, and Yong-Kim Chong 11 th Dec, 2014 ewsgan@ntu.edu.sg Digital Signal Processing Lab, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore

2. Contents 2 Introduction on feedback ANC Parallel-form narrowband feedback ANC Theoretical analysis on the use of error term Simulation results Conclusions and future works

3. Introduction on feedback ANC 3 Active noise control: introduce an anti-noise to cancel the primary noise source  Feedforward ANC – Reference microphone: not desired due to feedback of the secondary source or physically constraints – Non-acoustic sensors (e.g., tachometers)  Feedback ANC: internal model control (IMC) – Affected by frequency separation in primary noise; – Degraded by measurement noise and impulse noise; – Subject to secondary path estimation accuracy [5]; [5] V. L. Wang, W. S. Gan, A. W. H. Khong and S. M. Kuo, “Convergence Analysis of Narrowband Feedback ANC System With Imperfect Secondary Path Estimation,” IEEE Trans. Audio, Speech, Lang. Process., vol. 21, no. 11, pp. 2403-2411, Nov. 2013.

4. Parallel-form narrowband FBANC 4 [7] T. W. Wang, W. S. Gan, and S. M. Kuo, “New feedback active noise control system with improved performance,” Proc. IEEE ICASSP, Florence, Italy, 2014, pp. 6712-6716. Learning curves when the noise frequencies vary Effect of impulsive noise Compared to IMC based FBANC [7]:  increase frequency separation;  Improve convergence rate and noise reduction;  More robust to impulsive noise.

5. [9] C.-Y. Chang and S. M. Kuo, “Complete parallel narrowband active noise control systems,” IEEE Trans. Audio, Speech, Lang. Process., vol. 21, no. 9, pp. 1976–1986, Sep. 2013. Parallel-form narrowband FBANC 5 To use single full-band error or individual narrowband error? 2nd order IIR delayless filter bank [9]

6. Theoretical analysis 6 Consider using single full-band error Tones with different frequencies Taking expectation where disturbance

7. Simulations 7 Simulation setup 1: Assume perfect secondary path estimation, secondary path: s={1, -0.1, -0.2}; Primary noise: 4 tones (80, 160, 240, 320) Hz at sampling frequency 2 kHz; Four frequency channels are considered in parallel, one tone in each channel, and thus two taps are enough for the adaptive filters; For narrowband errors, an IIR filter bank similar to [9] is used, with p j =0.99; Step size = 0.1;

8. Result 1: Insignificance of D compared to P 8 Current iteration

9. Result 2: Weight adaptation 9 Channel 1 Channel 2 Channel 3 Channel 4

10. Result 3: Learning curves 10 Frequencies of the tones are: 80, 160, 240, and 320 Hz. Frequencies of the tones are: 40, 80, 120, and 160 Hz. Frequencies of the tones are: 100, 200, 300, and 400 Hz. Frequencies of the tones vary from 50, 100, 150, and 200 to 100, 200, 300, and 400 Hz. Using same step size, full-band error is better than narrowband error!

11. Simulation 2: setup 11 Assume perfect secondary path estimation, secondary path shown below; Primary noise: 4 tones with fundamental frequencies at 70, 80, 90, 100 Hz at sampling frequency 1.5 kHz; Four frequency channels are considered in parallel, one tone in each channel, and thus two taps are enough for the adaptive filters; For narrowband errors, IIR filter bank similar to [9] is used, with p j =0.95; Step size < 0.1* step size bound (theoretical);

12. More Results: different harmonics, small step size 12 Using a small enough step size, the converge performance between the two cases is quite close. 70, 140, 210, 280 Hz80, 160, 240, 320 Hz 90, 180, 270, 360 Hz 100, 200, 300, 400 Hz

13. Conclusions and Future work 13 We studied the use of error terms in parallel-form narrowband feedback active noise control: 1.Using different error terms, the MSE (hence noise reduction) performance is not affected; 2.The convergence performance differs: Using smaller enough step size (<0.1*bound), the performance of using full-band error and narrowband error is quite close; When the step size is larger, use of full-band single error yields faster convergence (in most of the cases); 3.When there is additional disturbance in the error microphone, the narrowband error could be better as it rejects the disturbance. 4.Future work shall investigate the exact conditions for the use of error terms with respect to the secondary path, frequencies of the primary noise, step size, etc.

14. More Results 14

15. More Results 15