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

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

Introduction on feedback ANC Active noise control: introduce an anti-noise to cancel the primary Introduction on feedback ANC Active noise control: introduce an anti-noise to cancel the primary noise source Ø Feedforward ANC – – Reference microphone: not desired due to feedback of the secondary source or physically constraints Non-acoustic sensors (e. g. , tachometers) Ø 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. 3

Parallel-form narrowband FBANC Compared to IMC based FBANC [7]: Ø increase frequency separation; Ø Parallel-form narrowband FBANC Compared to IMC based FBANC [7]: Ø increase frequency separation; Ø Improve convergence rate and noise reduction; Ø More robust to impulsive noise. Learning curves when the noise frequencies vary [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. Effect of impulsive noise 4

Parallel-form narrowband FBANC To use single full-band error or individual narrowband error? 2 nd Parallel-form narrowband FBANC To use single full-band error or individual narrowband error? 2 nd order IIR delayless filter bank [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. 5

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

Simulations Simulation setup 1: • Assume perfect secondary path estimation, secondary path: s={1, -0. Simulations Simulation setup 1: • Assume perfect secondary path estimation, secondary path: s={1, -0. 2}; • Primary noise: 4 tones (80, 160, 240, 320) Hz at sampling frequency 2 k. Hz; • 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 pj =0. 99; • Step size = 0. 1; 7

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

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

Result 3: Learning curves Frequencies of the tones are: 80, 160, 240, and 320 Result 3: Learning curves Frequencies of the tones are: 80, 160, 240, and 320 Hz. Frequencies of the tones are: 100, 200, 300, and 400 Hz. Frequencies of the tones are: 40, 80, 120, and 160 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! 10

Simulation 2: setup • Assume perfect secondary path estimation, secondary path shown below; • Simulation 2: setup • 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 k. Hz; • 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 pj =0. 95; • Step size < 0. 1* step size bound (theoretical); 11

More Results: different harmonics, small step size 70, 140, 210, 280 Hz 90, 180, More Results: different harmonics, small step size 70, 140, 210, 280 Hz 90, 180, 270, 360 Hz 80, 160, 240, 320 Hz 100, 200, 300, 400 Hz Using a small enough step size, the converge performance between the two cases is quite close. 12

Conclusions and Future work We studied the use of error terms in parallel-form narrowband Conclusions and Future work 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. 13

More Results 14 More Results 14

More Results 15 More Results 15