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Title Active noise cancellation headset.( Published version )
Author(s) Foo, Say Wei.; Senthilkumar, T. N.; Averty, Charles.
Citation
Foo, S. W., Senthilkumar, T. N., & Averty, C. (2005).
Active noise cancellation headset. IEEE International
Symposium on Circuits and Systems, ISCAS 2005: (pp.
268-271).
Issue Date 2009-07-03T02:45:10Z
URL http://hdl.handle.net/10220/4674
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Active Noise Cancellation Headset
Say-Wei Foo
1
,T N Senthilkumar
1
, and Charles Averty
2
1
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore.
2
ST Microelectronics Asia Pacific Ltd.
Abstract --In this paper, a new design for headset with active
noise cancellation capability is presented. For the proposed
headset, a Variable-Step-Size Normalized Least-Mean-Square
(VSS-NLMS) algorithm is adopted in the combined audio and
feedback active noise cancellation system. Experimental results
show that for the same set of signals, the average noise reduction
using the proposed adaptive algorithms is 38dB compared with
36dB using Normalized Least-Mean-Square algorithm and 14 dB
using the Least-Mean-Square algorithm. The speed of
convergence using the proposed approach is also faster compared
with the other two cases. Informal listening tests also favor the
adoption of the proposed VSS-NLMS adaptive algorithm.
Index Terms— active noise cancellation, audio signal, headset,
signal processing
I. INTRODUCTION
With the advances in consumer electronics, more and more
people listen to high quality pre-recorded music on the move using a
headset. However, if this is done in a noisy environment such as in a
flying aircraft or in a subway train, listening fatigue would soon set
in when the noise level is high. Research has been ongoing to
develop noise cancellation systems to reduce the noise level while
preserving the music level of the audio wave presented to the
eardrums.
For one such active noise cancellation (ANC) system, a
microphone is placed together with the loudspeaker inside the ear-
cup of the headset and a combined audio and feedback system is
introduced between the audio source and the special headset as
illustrated in Fig.1.
Fig. 1 Combined audio and ANC headset
The block diagram of a combined audio ANC system is depicted in
Fig.2. The essential operation of the feedback system is to produce a
signal that will nullify the external noise in the ear-cup of the headset.
For the system to work properly, it is assumed that the external noise
and the desired signal are uncorrelated and the magnitude of the
external noise entering the ear-cup should be less than what the
loudspeaker in the ear-cup can produce.
Fig.2 Block diagram of a generic combined audio and feedback ANC system
2680-7803-8834-8/05/$20.00 ©2005 IEEE.
In Fig.2, S(z) simulates the headset model. d(n) denotes the external
noise. The output signal, e(n), contains both the residual noise and the
desired audio signal, it is the signal presented to the eardrum and hence
should be as close to the desired audio signal as possible. The residual
noise e’(n) is separated from the output e(n), by adding the filtered
audio signal a’(n) from
ˆ
()Sz
. The audio signal is used as a reference
signal in the adaptive filter
ˆ
()Sz
. The adaptive filter
ˆ
()Sz
is called
the audio interference cancellation filter, since it is used to remove the
audio signal from e(n). Estimate of the secondary path model filter
ˆ
()Sz
is made offline using a white noise input. The estimate of the
noise, e’(n) is obtained by mixing e(n) with the desired audio signal
a’(n). The reference noise signal x(n) is extracted from e’(n). This
reference noise signal and the residual noise signal are fed to the
Shaping Algorithm, which computes the weights of the ANC filter
denoted by W(z) in the block diagram.
For ease of analysis, we shall assume that the audio signal a(n) is of
persistent excitation and uncorrelated with the primary noise d(n) and
that the audio interference cancellation filter
ˆ
()Sz
models the
secondary path filter
()Sz. The following derivations of the ANC
system can be made after convergence of the adaptive filter
ˆ
()Sz
[1].
ˆ
() () () ()
E
zEzSzAz
′
=+
(1)
() () ()()
E
zDzUzSz=− (2)
Substituting (2) into (1), we get
ˆ
() () ()() () ()
E
zDzUzSzSzAz
′
=− + (3)
As
() () ()Uz Az Yz=+, (3) can be written as
)()(
ˆ
)())()(()()(' zAzSzSzYzAzDzE ++−= (4)
If
ˆ
()Sz
is a perfect model of the secondary path, represented by
the filter
()Sz, that is,
ˆ
()Sz
= ()Sz, then (4) becomes,
() () ()()
E
zDzYzSz
′
=− (5)
D(z) represents the primary noise signal and the term
() ()YzSzrepresents the anti-noise signal. Hence ()
E
z
′
represents
the residual error signal of the ANC system.
The z-transform of the input reference noise signal, x(n), can be
written as,
ˆ
() () () ()Xz E z YzSz
′
=+
(6)
By substituting (5) into (6), we have
)(
ˆ
)()()()()( zSzYzSzYzDzX +−=
))()(
ˆ
)(()( zSzSzYzD −+=
(7)
If
ˆ
()Sz
= ()Sz, then ()
D
z = ()Xz. Thus, the reference noise
signal x(n) is identical to the external noise d(n).
II. THE SHAPING ALGORITHM
For the Shaping Algorithm as shown in Fig.2, Woon S. Gan and
Sen M. Kuo in their paper [1] investigated the case using Least Mean
Square (LMS) algorithm. However, the gain and step-size for the
LMS algorithm are fixed resulting in suboptimal performance when
the environment changes. Furthermore, unstable conditions may arise
when the noise level is high. To overcome these drawbacks, we
propose the adoption of a Variable Step-Size Normalized LMS (VSS-
NLMS) algorithm as the Shaping Algorithm. The basic principle of
operation of VSS-NLMS algorithm is that when the filter coefficients
are close to the optimum solution, a small step size is used; otherwise
a large step size is applied. For the experiments mentioned in this
paper, time-varying step-size parameter is changed in such a way that
the change is proportional to the negative of the gradient of the
squared estimation error with respect to the convergence parameter.
This algorithm reduces the trade-off between speed of convergence
and steady-state error.
Mathematically, the weights are adjusted according to the
following expression [2],
1
2
kk
kkk
k
eX
WW
X
µ
β
+
=+
+
(8)
where
k
µ
is the time-varying step-size and the error signal
k
e is
defined as,
T
kk kk
edXW=− (9)
The step-size sequence
k
µ
will be adapted using the following
expression,
2
1
1
2
k
kk
k
e
ρ
µµ
µ
−
−
∂
=−
∂
(10)
which can be transformed after, substituting (8) and (9) into (10), into
the following form.
1
11
2
1
T
kk
kk kk
k
XX
ee
X
µµ ρ
β
−
−−
−
=+
+
(11)
where
ρ
is a small positive constant that controls the behavior of the
step-size sequence
k
µ
.
In addition to VSS-NLMS, the performance of the
Normalized LMS (NLMS) algorithm is also investigated. The
NLMS algorithm was first introduced by Nagumo and Noda
[3]. In its simple form, the algorithm can be represented as
follows.
( ) ( ) ( )
T
yk W k X k= (12)
() () ()ek dk yk=− (13)
() ()
(1) ()
() ()
T
ek X k
Wk Wk
XkXk
α
γ
+= +
+
(14)
269
The term
α
is the normalized adaptation factor, its value is
chosen between 0 and 2.
γ
is a small positive term included to
ensure that the update term does not become excessively large
when the signal power
() ()
T
XkXk becomes small.
III. EXPERIMENTS AND PERFORMANCE COMPARISON
Experiments were carried out to assess the performance of the
LMS, NLMS and VSS-NLMS algorithms under different noisy
environments. For the noise control adaptive filter W(z), 128 taps are
used whereas the order of the secondary path adaptive filter is 75 taps.
The initial step size value chosen for NLMS is
α
= 0.004 and the
value of
γ
is chosen to be 0.05. The initial step size value chosen
for VSS-NLMS is 0.001 and the optimal value for constants
ρ
and
β
is 0.3. The values for
ρ
and
β
are critical. It is found that
inappropriate selection of these values will result in system instability.
For the case with subway train noise, the system is unstable when
LMS algorithm is adopted. The output waveforms when the ANC is
off and when the ANC is on using the NLMS and VSS-NLMS
algorithms are shown in Fig.A1 to Fig.A3 in Appendix A. The
residual noise for the two cases is shown in Fig.A4 and Fig.A5. The
magnitudes of noise reduction and the convergence rates for the three
algorithms under different noise environments are summarized in
Tables 1 and 2. For subway train noise, the performance of the system
using LMS algorithm is unstable and hence no values are given.
It can be observed that the VSS-NLMS algorithm efficiently
attenuates the noise signals by more than 37.6 dB compared to an
average of 36dB using NLMS and 14.2 dB using LMS. The
convergence rate of the VSS-NLMS algorithm is also much faster.
Informal listening tests also reveal that the quality of the audio signal
received is significantly better.
TABLE I
NOISE ATTENUATION (dB)
LMS NLMS VSS-NLMS
Helicopter noise 24 35 38
Jet air noise 12 31 33
Propeller air noise 20 37 38
Subway train noise Unstable 34 37
Car noise 10 39 41
Air hammer noise 5 38 38
Average (excluding
train noise)
14.2 36.0 37.6
TABLE II
RATE OF CONVERGENCE (No. of iterations)
LMS NLMS VSS-NLMS
Helicopter noise 22000 2470 1500
Jet air noise 120000 1350 1200
Propeller air noise 78000 750 640
Subway train noise Unstable 1700 1180
Car noise 240000 950 800
Air hammer noise 250000 270 150
The power spectral density of the noise present in the
corresponding frame of the signals shown in Figs.A1,A2 and A3 are
shown in Fig.3. From the figure, it can be observed that VSS-NLMS
gives the highest noise reduction.
IV. CONCLUSION
In this paper, a new algorithm is proposed for active noise
cancellation headset. The performance of the new algorithm, Variable
Step-Size Normalized LMS is compared with that of the LMS and
NLMS under different noisy environments. Results show that not only
the convergence of the VSS-NLMS is faster, but it also gives
significantly much better noise reduction under all the noisy
conditions tested. Informal listening tests also confirm the superiority
of the proposed algorithm.
ACKNOWLEDGEMENT
The authors would like to acknowledge the financial support given
by STMicroelectronics Asia Pacific Ltd. for this research.
REFERENCES
[1] Woon S. Gan and Sen M. Kuo, “An Integrated Audio and Active
Noise Control Headset”, IEEE Transactions on Consumer
Electronics, May 2002
[2] Ahmed I.Sulyman and Azzedine Zerguine, “Convergence and
Steady-State Analysis of a Variable Step-Size Normalized LMS
algorithm”, Proceedings of the Signal Processing and its
applications, July 2003.
[3] J. Nagumo and A. Noda, “ A learning method for system
identification”, IEEE Trans. Automat. Contr., vol. AC-12, no. 3,
pp 282-287, June 1967
[4] Theory and Design of Adaptive Filters, John R. Treicheler, C.
Richard Johnson, JR. Michael G. Larimore.
[5] Moshe Tarrab and Arie Feuer “Convergence and Performance
Analysis of the Normalized LMS Algorithm with Uncorrelated
Gaussian Data”, IEEE Transactions on Information Theory, July
1988
[6] Active Noise Reduction Headphone Systems by Chu Moy
[7] Sen M. Kuo and Dennis R. Morgan “Active Noise Control: A
Tutorial Review”, Proceedings of the IEEE, June 1999.
Fig.3 Spectrum showing noise reduction using NLMS
and VSS-NLMS algorithms
(Subway train noise)
270
APPENDIX A: WAVEFORMS OF SIGNALS (NOISE: SUBWAY TRAIN SOUND)
Fig.A1 Noise signal
Fig A2 Music signal
Fig A3 Output when ANC is OFF
Fig.A5 Output when ANC is ON (VSS-NLMS)
Fig A6 Residual noise (NLMS)
Fig.A7 Residual noise (VSS-NLMS)
271