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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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copyright holder. http://www.ieee.org/portal/site.

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