A Novel Approach for Single Microphone Active Noise Cancellation Bharath Siravara (1), Neeraj Magotra (1), Philip Loizou (2) (1) Texas Instruments Inc., (2) Department of Electrical Engineering 12500 TI Blvd., University of Texas at Dallas Dallas, TX 75243 P O Box 830688, EC33, Richardson, TX 75083
ABSTRACT This paper presents a novel approach for subband feedback Active Noise Control (ANC). Wideband ANC systems often involve adaptive filters with hundreds of taps. Using subband processing can considerably reduce the length of the adaptive filter. Conventional subband algorithms are generally based in the frequency domain and use at least 2 sensors. This paper presents a time domain algorithm for single sensor subband feedback ANC using relatively short fixed FIR filters to do the subband processing. The adaptive coefficients in the system are updated using a weight constrained NLMS algorithm for feedback ANC. The proposed subband algorithm had a significant performance advantage over the traditional single band ANC algorithm in terms of the rate of convergence and the noise attenuation that could be obtained
narrowband signals. As the bandwidth of the primary noise signal and the center frequency of the noise increases, the performance of the ANC system decreases [3]. Noise generated by motors, pumps, etc. tend to have a single dominant low frequency emphasis. However, there are many other sources of noise such as in the aircraft cockpits, automobile interiors, factory floors, etc. that tend to have a much wider bandwidth. Figure 1 shows the Power Spectral Density (psd) of noise recorded in an aircraft.
1. INTRODUCTION Over the past few decades there has been a tremendous increase in the level of ambient environmental noise. This has been primarily due to the growth of technology that has led to the proliferation of noisy engines, heavy machinery, pumps, high speed wind buffeting and a myriad other noise sources. Exposure to high decibels of sound proves damaging to humans from both a physical and a psychological aspect. The classical approach to noise cancellation is a passive acoustic approach. Passive silencing techniques such as sound absorption and isolation are inherently stable and effective over a broad range of frequencies. However, these tend to be expensive, bulky and generally ineffective for canceling noise at the lower frequencies. The steady increase in the performance of DSPs coupled with the decrease in their power consumption has enabled the use of DSPs in a variety of portable hearing enhancement devices such as hearing aids, headsets, hearing protectors, etc. Various signal processing techniques have been proposed over the years for noise reduction in the environment. One such technique to overcome this problem is Active Noise Cancellation (ANC), which is sound field modification by electracoustic means. ANC is an electroacoustic system that cancels the primary unwanted noise by introducing a canceling “antinoise” of equal amplitude but opposite phase, thus resulting in an attenuated residual noise signal [1] [2] [3]. ANC systems are based either on feedforward control where a coherent reference noise input is sensed or feedback control [4] where the controller does not have the benefit of a reference signal. In the case of headsets and hearing protectors, it is preferable not to have a reference sensor on the outer casing of the headphone. Hence the preferred algorithm is the feedback ANC algorithm. The traditional feedback ANC systems are most effective for low frequency periodic
Figure 1 PSD of noise recorded in an aircraft. Typical wideband ANC algorithms work best in the lower frequency bands and their performance deteriorates rapidly as the bandwidth and the center frequency of the noise increases. In this study, several experiments were performed to quantify the performance of feedback ANC systems as the frequency of the primary noise source increased A Knowles Electronic Manikin for Acoustic Research (KEMAR) was placed in a sound booth and the ANC headsets were placed on the KEMAR to make sound measurements that simulated those that would exist at the eardrums of a normal male listener. Using the calibrated system in the sound booth, colored noise at different center frequencies was played and the effective noise was recorded in the KEMAR with the ANC system on and the ANC system switched off. The experiments were repeated using commercially available ANC headsets from Bose and NCT. It was found that the headsets were very effective in reducing noise at the lower frequencies and the performance tailed off rapidly when the center frequency of the noise was increased beyond 500Hz. This problem can be addressed by using an adaptive system. Simulations were carried out in MATLAB for the single channel feedback ANC algorithm [1] and it was found that for smaller filter orders, the
performance of the adaptive system also deteriorated as the bandwidth and center frequency of the noise increased Thus to achieve significant noise attenuation over a wide band of frequencies the filter length needs to be inordinately large. Many new techniques have been proposed based on subband adaptive filtering [5] [6] [7]. Morgan [8] studied the application of these techniques to feedforward active noise control and proposed an alternate delayless subband ANC system [9][10] in which the subband filter weight update was done in the transform domain However, this technique does not translate very well to the feedback ANC system as it is very sensitive to any form of buffering and the performance of the algorithm deteriorates rapidly as the size of the buffer is increased. Further, since the reference signal is regenerated from the error signal, the delay in the auxiliary path does not have a detrimental effect on the performance of the feedback ANC system as long as the same delay is introduced into the path to the LMS update equation as well. In this paper, we propose a filter bank approach to subband filtering that provides significant computational advantages over the existing methods for feedforward subband ANC. Section 2 describes the proposed subband feedback ANC algorithm, section 3 discusses the implementation details and results obtained and section 4 gives a summary as well as avenues for future work.
2. Subband Feedback ANC The basic idea has been adopted from filterbank-based subband adaptive processing used in various applications. The residual error signal recorded is split into a number of bands using linear phase bandpass FIR filters and the FXLMS algorithm is applied to each of these bands separately. The antinoise signal produced by each of these blocks is then added before it is played from the speaker. Figure 2 shows the overall block diagram and Figure 3 shows the diagram for the modified FXLMS algorithm applied to each band.
d(n)
+ +
Σ
+
+ Σ
S(z)
Feedback ANC band 1
FIR
Feedback ANC band n
FIR
xi(n)
y(n)
Wi(z)
S^(z) S^(z)
Hi(z) xi’(n) di^(n)
yi’(n)
LMS
Hi(z)
+
Σ +
Figure 3 Modified feedback FXLMS algorithm applied to the ith band
3. Implementation and Results The system described in the previous section was implemented in MATLAB and simulations were carried out using various input signals. The single band FXLMS algorithm [1] was implemented in MATLAB and this formed the basis of the subband technique as well as serving as a comparative algorithm. A simple LMS algorithm with a small stepsize of 0.0005 was used. The secondary path transfer function S(z) was estimated using an offline modeling technique. A pair of ANC headsets was hooked up to a DHP100 EVM [12] and a simple LMS algorithm was implemented in fixed point C to do the system identification. The estimated secondary path Sˆ ( z ) was used for both the true secondary path transfer function S(z) as well as the estimate. Hence, ideal conditions were assumed implicitly in that there was no error in the estimation of the secondary path. The magnitude response of the secondary path transfer function is shown in Figure 4.
e(n)
-
Figure 2 Proposed Subband feedback ANC system using filterbanks.
e(n)
Figure 4 Frequency response of the secondary path transfer function S(z).
The advantages of using the normalized LMS algorithm are well documented for faster convergence and a lower mean squared error [11]. The NLMS algorithm was used in the feedback ANC system and proved to be unstable in its regular form as the step size tended to approach the upper bounds of the theoretical permissible step size especially in the initial stages. To circumvent this problem, a constrained NLMS algorithm was used where the step size was saturated at a certain value. The constrained NLMS algorithm was found to perform much better when compared to the LMS algorithm. The step size of the adaptive filter was calculated as [3]
µ =
L pi * P + ∆
(1)
where pi is the instantaneous power of the input signal, P is the length of the adaptive filter and ∆ is the delay introduced by the secondary path transfer function S(z). The instantaneous power of the input signal pi was calculated as the magnitude squared of the input signal:
σ x2 (n) = βσ x2 (n − 1) + (1 − β ) x 2 (n)
(2)
where β is a constant with a value of 0.9. The power was also estimated using the Teager energy operator as shown in equation 3. However, there was no performance improvement in using this method and hence the conventional method as shown in equation 2 was used.
Ψd ( x[n]) = x 2 [n] − x[n − 1]x[n + 1]
(3)
Simulations were also carried out to determine the optimal length of the adaptive filter used, for the feedback FXNLMS algorithm. The optimal filter length for the FXNLMS algorithm was found to be 12. The FXNLMS algorithm described here formed as the basis for the subband ANC system. The bandpass filtering was done using linear phase FIR filters. Interestingly, it was found that convergence could still be achieved with filter lengths of up to a 100 taps. The number of bands needed and the bandwidth of each band would be determined largely by the characteristic of the noise that needs to be cancelled and the specific application of the ANC system. The system was tested using colored noise at different center frequencies and a bandwidth of 250Hz. The simplest system used included two distinct bands, one for noise below 1kHz and one for noise above 1kHz. Significant performance improvements were found using even this simple system. Further, it was found that with careful design of the bandpass filters, the effective bandwidth over which noise attenuation could be achieved was significantly increased. As long as the bandpass filters had a sufficiently narrow bandwidth and the signal spectrum was covered by a sufficiently large number of bands, it was possible to achieve noise attenuation up to 4kHz. The tradeoff to the increased bandwidth was a slight decrease in convergence time at the lower frequencies. The stability of the system was found to be largely dependent on the design of the filters used to split the signal into subbands. The system was first evaluated using sine waves at different frequencies. The frequency of the input sinusoids was chosen so as to represent the entire gamut of the frequency spectrum of
interest. If f1 and f2 are the two frequencies of interest, the input noise signal d(n) was computed as
d (n) = cos(2π
f1 f n) + cos(2π 2 n) fS fS
(4)
where fs is the sampling frequency. The single band FXLMS algorithm and the subband FXNLMS algorithm were then simulated using the signal generated according to equation 4 as the input. The MSE plots were then calculated by ensemble averaging the residual error signals over 512 separate runs with the input signal shifted slightly in phase at each trial. It was found that the performance of the single band system was strongest at the lower frequencies and gradually tapered off as the frequency of the noise increased. The performance of the subband system was then evaluated using sine waves at two distinct frequencies. The subband system was found to have a significantly faster convergence time when compared to the single band method. To further validate the performance of the subband ANC method, simulations were carried out using artificially generated colored noise as input. The signals were generated by first generating white noise using the MATLAB rand command and then filtered using 4th order IIR filters with a fixed bandwidth of 250Hz and an 60dB roll off , with different center frequencies. Time plots and MSE plots were generated for each of these files. The MSE plots were generated by ensemble averaging the residual error signals over 16 different runs of each algorithm. Figures 5 and 6 show the MSE plots and time plots of the residual noise signal for noise at 500-750Hz and 15001750Hz. The performance of the subband system for noise at different frequencies is summarized in Table 2. Noise Noise attenuation attenuation Frequency of primary of single band of subband noise signal algorithm algorithm 0-250Hz
14.4dB
16dB
500-750Hz and 12501500Hz
5.66dB
10.03dB
750-1000Hz and 20002250Hz
6.31dB
11.9dB
3000-3250Hz
9.7dB
15.79dB
The subband ANC algorithm was found to perform much better across all frequencies. The performance of the subband system was significantly better when colored noise residing in different frequency regions were combined. Since most real world ambient noise tends to be wideband with more than one dominant frequency, the subband system would be expected to have a much bigger performance advantage for real world signals. More details about the implementation and performance of the proposed subband ANC algorithm can be found in [3].
Our simulation results obtained by using colored noise at different frequencies, showed, that by carefully choosing the individual bands, the subband ANC algorithm can provide significant improvement in performance. Our future work includes quantization analysis of the proposed algorithm and its implementation on a TI real time DSP system
5. REFERENCES
Figure 5 MSE plots for noise at 500-750Hz and 12501500Hz
[1]
S.M. Kuo and D.R. Morgan, Active Noise Control: a tutorial review, Proceedings of the IEEE, Volume 87, Number 6, June 1999.
[2]
S.M. Kuo and D.R. Morgan, Active Noise Control Systems: algorithms and DSP implementations, John Wiley and Sons, New York, 1996
[3]
B. Siravara, Subband Feedback Active Noise Control, Masters Thesis, University of Texas at Dallas, 2002.
[4]
D. Vijayan, Feedback Active Noise Control Systems, Masters thesis, Northern Illinois University, 1994.
[5]
A. Gilloire and M. Vetterli, Adaptive Filtering in subbands, Proc. ICASSP, Vol. 3, pp. 1572-1575, 1988. B.E. Usevitch and M.T. Orchard, Adaptive Filtering using Filter Banks, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 43, No. 3, March 1996. M.R. Petraglia and R.G. Alves, New Results on Adaptive Filtering Using Filter Banks, IEEE International Symposium on Circuits and Systems, 1997. D.R. Morgan, An Analysis of Multiple Correlation Cancellation Loops with a Filter in the Auxiliary Path, IEEE Transactions of Acoustic, Speech and Signal Processing, Volume ASSP-28, Number 4, August 1980.
[6]
[7]
[8]
Figure 6 PSD of input noise(top panel) and time plots of the residual signals obtained using the single-band FXLMS algorithm (middle panel) and the two-band FXLMS algorithm (bottom panel).
[9] [10]
.
4. CONCLUSIONS AND FUTURE WORK The major drawback of traditional single band ANC algorithms is that their performance deteriorates rapidly as the frequency of the noise increases. However, noise in real world conditions tends to be broadband with significant high frequency components. Our simulation results proved that by carefully considering the number of bands and their respective bandwidth, significant noise attenuation could be achieved using the proposed subband ANC algorithm even at the higher frequency regions. Further, as the bandwidth of the noise increased, the performance advantage of the subband ANC algorithm over the single band system was more pronounced. Real world noise due to engines, heavy machinery, etc. tends to have distinct frequency components that are well separated in the frequency spectrum.
D.R. Morgan and J C Thi, A Delayless Subband Adaptive Filter Architecture, IEEE Transactions on Signal Processing, Vol. 43, No. 8, August 1995. S.J. Park, J.H. Yun, Y.C. Park D.H. Youn, A Delayless Subband Active Noise Control System for Wideband Noise Control, IEEE Transactions on Speech and Audio Processing, Vol. 9, No. 8, November 2001.
[11] B. Widrow and S.D. Stearns, Adaptive Signal Processing, Prentice-Hall, Inc. Englewood Cliffs, N.J, 1985.
[12]
Texas Instruments Inc., DHP Hearing Development Kit for DHP 100 Users Guide, SPRU551, September 2001.
