some practical insights in multichannel active noise control equalization
SOME PRACTICAL INSIGHTS IN MULTICHANNEL ACTIVE NOISE CONTROL EQUALIZATION Maria de Diego, Alberto Gonzalez, Clemente Garcia and Miguel Ferrer
Dept. of Comunicaciones, Universidad Politecnica de Valencia 46071 Valencia, SPAIN. e-mail: [email protected]
ABSTRACT
In this paper, a novel adaptive algorithm for equalization of periodic signals using active control is developed. This algorithm actively cancels out a single frequency without changing the amplitude levels at close frequencies. The algorithm performance is compared with that of an adaptive equalizer previously reported [1][2]. Both algorithms are used for a real multichannel system in order to equalize some given frequencies of a primary signal. The local active noise control system has been used to create an equalization zone. A two channels system is used and the total pressure is controlled at two microphones. A 4100 type Bruel manikin with two calibrated microphones at the ear canals has been used to obtain sound levels in an hypothetic listeners ears. The equalization points are not only the error sensors positions but an area around them which is measured using the manikin.
1. INTRODUCTION In a conventional active noise control system, the pressure signal at a single cancellation microphone, named as error signal, is cancelled out by the action of a secondary source that creates a zone of quiet around of this point. The ltered-X LMS algorithm [3] (FXLMS) and its multichannel version, the multiple error LMS algorithm [4] (MELMS), have been the most widely used adaptive ltering strategies applied to single or multiple channel active noise control systems for narrowband applications [5]. For periodic signals these algorithms become adaptive notch lters that remove the most powerful spectral components of the primary signal for frequencies below 500 Hz. The stability of the adaptive notch lters using the FXLMS algorithm has been analyzed in [6][7]. Nevertheless, it can be desirable to retain a small residual error in order to create a speci c acoustic eld in some applications. For example, inside a vehicle, driver could prefer to listen some audible information instead of quiet, to improve safety or This work was supported by CICYT, grant TIC98-0343
to feel more comfortable. It can be guessed that key issue is to amplify or attenuate independently each single frequency in order to reshape the sound eld. An active noise equalizer was proposed in [1][2] which uses the FXLMS algorithm to adapt the coecients of two-weights lters minimizing a pseudo-error signal instead of the residual noise. This FXLMS active noise equalizer was applied to a single-input active noise control system in [1]. The fact is that this algorithm is unable to control independently close frequencies (i.e. to cancel one and leave the others unchanged). It can be shown that the active equalizer transfer function does not secure this. However, the proposed approach has the property of being able to force zeros of its transfer function without changing the amplitude levels at close frequencies. This can be achieved just modifying the pseudo-error signal. The behaviour of both algorithms was analyzed and compared. The ability of the local active noise control system with two secondary sources and two error sensors to create equalization zones is examined. A 4100 type Bruel dummy head and torso was moved using a linear movement platform with two step-by-step engines in order to measure the residual noise levels in the area where the local control system was controlling the acoustic eld. This paper is organized as follows. We rst comment the multichannel version of the FXLMS active noise equalizer described in [1][2]. Then modi cations of the original algorithm are brie y presented. Section 4 describes the practical system developed for the active equalization of engine noise. Paper ends analyzing the equalization noise levels achieved using both algorithms.
2. ACTIVE NOISE CONTROL EQUALIZER A detailed development of the multichannel extension of the FXLMS active noise equalizer algorithm described in [1][2] is quite cumbersome, because the original algorithm becomes a three dimensional one with K refer-
Figure 1: Multichannel narrowband feedforward active noise equalization system. ence signals (single tones), M secondary sources and L error sensors, see the block diagram of gure 1. A set of reference signals is generated from the information provided by a synchronization signal. Let us assume that K pure cosine waves are generated as follows,
xk [n] = Ak cos(wk n + k ); k = 1; :::; K (1) where Ak and k are respectively the amplitude and phase of the k-th reference signal of frequency wk . There are M two-weight lters for each reference signal, being ymk [n] the m-th lter output of the k-th signal.
The mean square of the sum of pseudo-error signals will be minimized by the algorithm. A pseudo-error is obtained as,
e0lmk [n] = el [n] + k fs^lm[n] ymk [n]g (2) l = 1; :::; L; m = 1; :::; M where el [n] is the l-th residual noise component, k is the k-th gain parameter that determines the amplitude of the k-th residual harmonic, ( k = 0 cancellation, 0 < k < 1 attenuation and k = 1 pass mode) and s^lm [n] is the impulse response function of the estimated secondary path model S^lm (z ) from the m-th secondary source to the l-th error sensor. For the k-th reference signal, the coecients update equations of the m-th adaptive lter are given by,
Figure 2: Block diagram of a single-channel novel active noise equalizer. version of the algorithm can be achieved if a common pseudo-error signal is used, gure 2 shows the block diagram of the novel single channel active noise equalizer. On its multichannel version, there is a single pseudoerror signal for each secondary path. That is,
e0lm [n] = el [n] +
XK kfs^lm[n] ymk[n]g k=1
(5)
which can be easily compared with equation (2). For the k-th reference signal, the coecients update equations of the m-th adaptive lter are then given by,
XL e0lm[n]fxk[n] s^lm[n]g (6) L X w [ n + 1] = w [ n ] ; 2 km km 0 wkm [n + 1] = wkm [n] ; 2 elmk [n]fxk [n] s^lm [n]g (3) l l L X L X w ^ [ n + 1] = w ^ [ n ] ; 2 e0lm [n]fx^k [n] s^lm [n]g (7) km w^km [n + 1] = w^km [n] ; 2 e0lmk [n]fx^k [n] s^lm [n]g (4) km =1
l=1
3. NOVEL ACTIVE NOISE CONTROL EQUALIZER The FXLMS active noise equalizer of the previous section can be modi ed to improve its behaviour. A new
=1
l=1
Computer simulations can show the performance of the novel active noise equalizer in case of two very close frequencies when the gain parameter vector, B, is [0 1] in order to cancel one frequency and retain the other. The k-th element of the gain parameters vector B, is the kth gain parameter k that determines the amplitude of k-th residual harmonic. Figure 3 shows the response of
the experimental transfer function H (z ) (de ned as the ratio between the z -transforms of error signal E (z ) and primary noise D(z )) obtained in a single-channel system for both algorithms where the parameters setting are: f1 = 0:0175, f2 = 0:035 (normalized frequencies, sampling frequency=1), = 6 10;2 and B=[0 1]. The amplitude of the signal of frequency f1 is completely eliminated but the amplitude of the signal of frequency f2 is only unchanged using the new approach (see gure 3.(b)). Active noise equalizer
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Figure 4: Manikin and platform used in the measurements and the array of up to four microphones as error sensors.
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ing ANC system operation, see gure 4. The primary loudspeaker and the two secondary sources were located facing the manikin in the direction of the largest horizontal dimension of the room. The ANC control algorithms were implemented on a DSP card.
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Figure 3: Amplitude response of the experimental transfer function H (z ): (a) active noise equalizer and (b) new approach.
4. PROTOTYPE DESCRIPTION The local ANC system was tested in a wooden listening chamber of dimensions 2:3 m x1:8 m x2:4 m. An array of up to four microphones was mounted on an hypothetical headrest of a seat. The manikin rested on a surface moved by a lineal movement platform with two step-by-step engines in order to measure the residual noise levels in the area around the local system dur-
Let us consider a control system with one primary source, two secondary sources and two error sensors (1:2:2 system). The noise to be cancelled is engine noise (obtained at 1200 r.p.m., repetitive noise with harmonics of 20 Hz). The power spectral density of the signal measured at the left manikin's microphone, which does not take part of the control system, for different gain parameters vectors are shown on gure 5. The gain parameters vectors used were B=[0 ... 0] ( gure 5.(a)) and B=[1 1 0 0.8 0.3 0.3 0.2 0.1 0 0 0] ( gure 5.(b)). The shown test was performed by means of the modi ed active noise control equalizer. Zones of equalization are obtained by sampling an area of about 30 x 30 cm2 using the manikin and the movable platform. The primary signal was again repetitive noise with harmonics of 20 Hz. Noise reduction levels were measured in the area at the right manikin's microphone after cancellation (B=[0 ... 0]). A general attenuation of about 30 dB was achieved at every frequencies. Figure 6 shows noise reductions levels observed for the fourth harmonic (80 Hz) in the analyzed area using the novel multichannel active noise equalizer. In this case the achieved attenuation was signi cantly more than 30 dB because of the high level of the the fourth harmonic.
beta=zeros(1,10), 2:2 system, left microphone
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Figure 6: Attenuations achieved for the fourth harmonic (80 Hz) at right manikins microphone after the ANC system operation in order to cancel car engine noise using the novel multichannel active noise equalizer. Sampling rate 500 Hz. Cut-o frequency 230 Hz.
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7. REFERENCES
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Figure 5: Power spectral density of the signal measured at the left manikins microphone in a 1:2:2 system in the listening room before the ANC system operation (solid line), after the ANC system operation (dashed line) with engine noise using the novel multichannel active noise control equalizer (a) B=[0 ... 0] and (b) B=[1 1 0 0.8 0.3 0.3 0.2 0.1 0 0 0 ]. Arbitrary units. Sampling rate 500 Hz. Cut-o frequency 230 Hz.
6. CONCLUSIONS A multichannel active noise control equalizer has been developed and implemented on a practical system. A novel multichannel equalizer has been proposed that has the property of independently controlling very close frequencies by de ning a modi ed pseudo-error signal. Experimental veri cation tests with di erent parameters setting validate the use of the developed algorithm. Results demonstrate that is possible to conform the acoustic eld around the error sensors and that the equalization zones obtained are large enough to cover listeners head motion. Furthermore, the practical ANC system allows manikin movements without a ecting algorithms' stability.
[1] Sen M. Kuo and Min J. Ji. Development and analysis of an adaptive noise equalizer. IEEE Trans. on Speech and Audio Processing, 3(3):217{222, May 1995. [2] S. Kuo and D. Morgan. Active Noise Control Systems. John Wiley- Sons, 1996. [3] B. Widrow and S.D. Stearns. Adaptive Signal Processing. Englewood Cli s, N.J: Prentice -Hall, 1985. [4] S. J. Elliott, I. M. Stothers, and P.A. Nelson. A multiple error lms algorithm and its application to the active control of sound and vibration. IEEE Trans. Acoust. Speech Signal Processing, 35(10):1423{1434, october 1987. [5] M. de Diego, A. Gonzalez, and C. Garcia. On the performance of a local active noise control system. Proc. ICASSP-99, march 1999. [6] D. Morgan and C. Sanford. A control theory approach to the stability and transient analysis of the ltered-x lms adaptive notch lter. IEEE Trans. on signal processing, 40(9):2341{2346, september 1992. [7] X. Kong and S. Kuo. Study of causality constraint on feedforward active noise control systems. IEEE Transactions on circuits and systems-II: analog and digital signal processing, 46(2):183{186, February 1999.
Dept. of Comunicaciones, Universidad Politecnica de Valencia 46071 Valencia, SPAIN. e-mail: [email protected]
ABSTRACT
In this paper, a novel adaptive algorithm for equalization of periodic signals using active control is developed. This algorithm actively cancels out a single frequency without changing the amplitude levels at close frequencies. The algorithm performance is compared with that of an adaptive equalizer previously reported [1][2]. Both algorithms are used for a real multichannel system in order to equalize some given frequencies of a primary signal. The local active noise control system has been used to create an equalization zone. A two channels system is used and the total pressure is controlled at two microphones. A 4100 type Bruel manikin with two calibrated microphones at the ear canals has been used to obtain sound levels in an hypothetic listeners ears. The equalization points are not only the error sensors positions but an area around them which is measured using the manikin.
1. INTRODUCTION In a conventional active noise control system, the pressure signal at a single cancellation microphone, named as error signal, is cancelled out by the action of a secondary source that creates a zone of quiet around of this point. The ltered-X LMS algorithm [3] (FXLMS) and its multichannel version, the multiple error LMS algorithm [4] (MELMS), have been the most widely used adaptive ltering strategies applied to single or multiple channel active noise control systems for narrowband applications [5]. For periodic signals these algorithms become adaptive notch lters that remove the most powerful spectral components of the primary signal for frequencies below 500 Hz. The stability of the adaptive notch lters using the FXLMS algorithm has been analyzed in [6][7]. Nevertheless, it can be desirable to retain a small residual error in order to create a speci c acoustic eld in some applications. For example, inside a vehicle, driver could prefer to listen some audible information instead of quiet, to improve safety or This work was supported by CICYT, grant TIC98-0343
to feel more comfortable. It can be guessed that key issue is to amplify or attenuate independently each single frequency in order to reshape the sound eld. An active noise equalizer was proposed in [1][2] which uses the FXLMS algorithm to adapt the coecients of two-weights lters minimizing a pseudo-error signal instead of the residual noise. This FXLMS active noise equalizer was applied to a single-input active noise control system in [1]. The fact is that this algorithm is unable to control independently close frequencies (i.e. to cancel one and leave the others unchanged). It can be shown that the active equalizer transfer function does not secure this. However, the proposed approach has the property of being able to force zeros of its transfer function without changing the amplitude levels at close frequencies. This can be achieved just modifying the pseudo-error signal. The behaviour of both algorithms was analyzed and compared. The ability of the local active noise control system with two secondary sources and two error sensors to create equalization zones is examined. A 4100 type Bruel dummy head and torso was moved using a linear movement platform with two step-by-step engines in order to measure the residual noise levels in the area where the local control system was controlling the acoustic eld. This paper is organized as follows. We rst comment the multichannel version of the FXLMS active noise equalizer described in [1][2]. Then modi cations of the original algorithm are brie y presented. Section 4 describes the practical system developed for the active equalization of engine noise. Paper ends analyzing the equalization noise levels achieved using both algorithms.
2. ACTIVE NOISE CONTROL EQUALIZER A detailed development of the multichannel extension of the FXLMS active noise equalizer algorithm described in [1][2] is quite cumbersome, because the original algorithm becomes a three dimensional one with K refer-
Figure 1: Multichannel narrowband feedforward active noise equalization system. ence signals (single tones), M secondary sources and L error sensors, see the block diagram of gure 1. A set of reference signals is generated from the information provided by a synchronization signal. Let us assume that K pure cosine waves are generated as follows,
xk [n] = Ak cos(wk n + k ); k = 1; :::; K (1) where Ak and k are respectively the amplitude and phase of the k-th reference signal of frequency wk . There are M two-weight lters for each reference signal, being ymk [n] the m-th lter output of the k-th signal.
The mean square of the sum of pseudo-error signals will be minimized by the algorithm. A pseudo-error is obtained as,
e0lmk [n] = el [n] + k fs^lm[n] ymk [n]g (2) l = 1; :::; L; m = 1; :::; M where el [n] is the l-th residual noise component, k is the k-th gain parameter that determines the amplitude of the k-th residual harmonic, ( k = 0 cancellation, 0 < k < 1 attenuation and k = 1 pass mode) and s^lm [n] is the impulse response function of the estimated secondary path model S^lm (z ) from the m-th secondary source to the l-th error sensor. For the k-th reference signal, the coecients update equations of the m-th adaptive lter are given by,
Figure 2: Block diagram of a single-channel novel active noise equalizer. version of the algorithm can be achieved if a common pseudo-error signal is used, gure 2 shows the block diagram of the novel single channel active noise equalizer. On its multichannel version, there is a single pseudoerror signal for each secondary path. That is,
e0lm [n] = el [n] +
XK kfs^lm[n] ymk[n]g k=1
(5)
which can be easily compared with equation (2). For the k-th reference signal, the coecients update equations of the m-th adaptive lter are then given by,
XL e0lm[n]fxk[n] s^lm[n]g (6) L X w [ n + 1] = w [ n ] ; 2 km km 0 wkm [n + 1] = wkm [n] ; 2 elmk [n]fxk [n] s^lm [n]g (3) l l L X L X w ^ [ n + 1] = w ^ [ n ] ; 2 e0lm [n]fx^k [n] s^lm [n]g (7) km w^km [n + 1] = w^km [n] ; 2 e0lmk [n]fx^k [n] s^lm [n]g (4) km =1
l=1
3. NOVEL ACTIVE NOISE CONTROL EQUALIZER The FXLMS active noise equalizer of the previous section can be modi ed to improve its behaviour. A new
=1
l=1
Computer simulations can show the performance of the novel active noise equalizer in case of two very close frequencies when the gain parameter vector, B, is [0 1] in order to cancel one frequency and retain the other. The k-th element of the gain parameters vector B, is the kth gain parameter k that determines the amplitude of k-th residual harmonic. Figure 3 shows the response of
the experimental transfer function H (z ) (de ned as the ratio between the z -transforms of error signal E (z ) and primary noise D(z )) obtained in a single-channel system for both algorithms where the parameters setting are: f1 = 0:0175, f2 = 0:035 (normalized frequencies, sampling frequency=1), = 6 10;2 and B=[0 1]. The amplitude of the signal of frequency f1 is completely eliminated but the amplitude of the signal of frequency f2 is only unchanged using the new approach (see gure 3.(b)). Active noise equalizer
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Figure 4: Manikin and platform used in the measurements and the array of up to four microphones as error sensors.
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5. EXPERIMENTAL RESULTS
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ing ANC system operation, see gure 4. The primary loudspeaker and the two secondary sources were located facing the manikin in the direction of the largest horizontal dimension of the room. The ANC control algorithms were implemented on a DSP card.
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Figure 3: Amplitude response of the experimental transfer function H (z ): (a) active noise equalizer and (b) new approach.
4. PROTOTYPE DESCRIPTION The local ANC system was tested in a wooden listening chamber of dimensions 2:3 m x1:8 m x2:4 m. An array of up to four microphones was mounted on an hypothetical headrest of a seat. The manikin rested on a surface moved by a lineal movement platform with two step-by-step engines in order to measure the residual noise levels in the area around the local system dur-
Let us consider a control system with one primary source, two secondary sources and two error sensors (1:2:2 system). The noise to be cancelled is engine noise (obtained at 1200 r.p.m., repetitive noise with harmonics of 20 Hz). The power spectral density of the signal measured at the left manikin's microphone, which does not take part of the control system, for different gain parameters vectors are shown on gure 5. The gain parameters vectors used were B=[0 ... 0] ( gure 5.(a)) and B=[1 1 0 0.8 0.3 0.3 0.2 0.1 0 0 0] ( gure 5.(b)). The shown test was performed by means of the modi ed active noise control equalizer. Zones of equalization are obtained by sampling an area of about 30 x 30 cm2 using the manikin and the movable platform. The primary signal was again repetitive noise with harmonics of 20 Hz. Noise reduction levels were measured in the area at the right manikin's microphone after cancellation (B=[0 ... 0]). A general attenuation of about 30 dB was achieved at every frequencies. Figure 6 shows noise reductions levels observed for the fourth harmonic (80 Hz) in the analyzed area using the novel multichannel active noise equalizer. In this case the achieved attenuation was signi cantly more than 30 dB because of the high level of the the fourth harmonic.
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Figure 6: Attenuations achieved for the fourth harmonic (80 Hz) at right manikins microphone after the ANC system operation in order to cancel car engine noise using the novel multichannel active noise equalizer. Sampling rate 500 Hz. Cut-o frequency 230 Hz.
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7. REFERENCES
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Figure 5: Power spectral density of the signal measured at the left manikins microphone in a 1:2:2 system in the listening room before the ANC system operation (solid line), after the ANC system operation (dashed line) with engine noise using the novel multichannel active noise control equalizer (a) B=[0 ... 0] and (b) B=[1 1 0 0.8 0.3 0.3 0.2 0.1 0 0 0 ]. Arbitrary units. Sampling rate 500 Hz. Cut-o frequency 230 Hz.
6. CONCLUSIONS A multichannel active noise control equalizer has been developed and implemented on a practical system. A novel multichannel equalizer has been proposed that has the property of independently controlling very close frequencies by de ning a modi ed pseudo-error signal. Experimental veri cation tests with di erent parameters setting validate the use of the developed algorithm. Results demonstrate that is possible to conform the acoustic eld around the error sensors and that the equalization zones obtained are large enough to cover listeners head motion. Furthermore, the practical ANC system allows manikin movements without a ecting algorithms' stability.
[1] Sen M. Kuo and Min J. Ji. Development and analysis of an adaptive noise equalizer. IEEE Trans. on Speech and Audio Processing, 3(3):217{222, May 1995. [2] S. Kuo and D. Morgan. Active Noise Control Systems. John Wiley- Sons, 1996. [3] B. Widrow and S.D. Stearns. Adaptive Signal Processing. Englewood Cli s, N.J: Prentice -Hall, 1985. [4] S. J. Elliott, I. M. Stothers, and P.A. Nelson. A multiple error lms algorithm and its application to the active control of sound and vibration. IEEE Trans. Acoust. Speech Signal Processing, 35(10):1423{1434, october 1987. [5] M. de Diego, A. Gonzalez, and C. Garcia. On the performance of a local active noise control system. Proc. ICASSP-99, march 1999. [6] D. Morgan and C. Sanford. A control theory approach to the stability and transient analysis of the ltered-x lms adaptive notch lter. IEEE Trans. on signal processing, 40(9):2341{2346, september 1992. [7] X. Kong and S. Kuo. Study of causality constraint on feedforward active noise control systems. IEEE Transactions on circuits and systems-II: analog and digital signal processing, 46(2):183{186, February 1999.
