Bharath Ms Thesis

7/31/2019 Bharath Ms Thesis

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SUBBAND FEEDBACK ACTIVE NOISE CANCELLATION

APPROVED BY SUPERVISORY COMMITTEE:

Dr. Philip C. Loizou, Chair

Dr. Louis R. Hunt

Dr. Nasser Kehtarnavaz


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Copyright 2002

Bharath M Siravara

All Rights Reserved


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by

Bharath M Siravara, B.E.

THESIS

Presented to the Faculty of

The University of Texas at Dallas

in Partial Fulfillment

of the Requirements

for the Degree of

MASTER OF SCIENCE IN ELECTRICAL ENGINEERING

THE UNIVERSITY OF TEXAS AT DALLAS

August 2002


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ACKNOWLEDGEMENTS

I would like to thank my advisor Dr. Philip C. Loizou for providing me with the

opportunity to work over the past two years as a Research Assistant in the Speech

Processing Research Laboratory, Department of Electrical Engineering. I thank him for

the guidance he has provided and the confidence he has shown in my work.

I would like to express my gratitude to Dr. Louis R. Hunt and Dr. Nasser Kehtarnavaz for

serving on my committee.

I would like to thank Dr. Emily Tobey at the Advanced Hearing Research Center for

providing with an opportunity to work at Callier and for the support and guidance that

she provided throughout my career at graduate school. I would also like to thank the

engineers audiologist Paul Dybala for helping me with numerous experiments at Callier.

I would like to express my deepest gratitude to Dr. Neeraj Magotra of Texas Instruments,

Dallas for sparking my interest in DSP. I thank him for the invaluable guidance and

support that he has provided in both my professional and personal life and for the

confidence that he has shown in my abilities. I look forward to working with him in the

years to come.

I would also like to thank all the members of the Speech Processing Laboratory for their

timely help and support. I would like to thank my entire family and all my friends for

supporting and standing by me through the years. This research was supported by a gift to

the University of Texas at Dallas from Texas Instruments.

August 2002.


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Bharath M Siravara, M.S.E.E.

The University of Texas at Dallas, 2002

This thesis presents a new technique for subband feedback active noise control. The

problem of controlling the noise level in the environment has been the focus of a

tremendous amount of research over the years. Active Noise Cancellation (ANC) is one

such approach that has been proposed for reduction of steady state noise. ANC refers to

an electromechanical or electroacoustic technique of canceling acoustic disturbance to

yield a quieter environment. The basic principle of ANC is to introduce a canceling

antinoise signal that has the same amplitude but the exact opposite phase, thus resulting

in an attenuated residual noise signal. Wideband active noise control systems often

involve adaptive filter lengths 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 thesis

presents a time domain algorithm for single sensor subband feedback ANC targeted for

use in headsets and hearing protectors. The subband processing is done using relatively

short fixed FIR filters. The algorithm also adopts the weight constrained NLMS

algorithm for feedback ANC. Results showed that the proposed subband feedback ANC

algorithm outperformed the traditional single band ANC system.


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TABLE OF CONTENTS

ACKNOWLEDGEMENTS ............................................................................................... iv

ABSTRACT........................................................................................................................ v

TABLE OF CONTENTS...................................................................................................vi

LIST OF FIGURES...........................................................................................................vii

CHAPTER 1 - INTRODUCTION...................................................................................... 1

CHAPTER 2 - LITERATURE SURVEY........................................................................... 4

2.1 Broadband feedforward Active Noise Control.......................................................... 52.2 Narrowband Feedforward ANC................................................................................ 92.3 Feedback Active Noise Control .............................................................................. 102.3 Multi channel Active Noise Cancellation ............................................................... 212.4 Frequency Domain and Subband Active Noise Cancellation................................. 23

CHAPTER 3 - SUBBAND ACTIVE NOISE CANCELLATION................................... 27

3.1 Motivation ............................................................................................................... 273.2 Secondary Path Modeling ....................................................................................... 323.3 Filtered X-LMS algorithm ...................................................................................... 35

3.4 Subband Active Noise Cancellation System........................................................... 40CHAPTER 4 - RESULTS................................................................................................. 45

4.1 Performance of the Subband ANC system with sine waves ................................... 474.2 Performance of the subband ANC algorithm for colored noise.............................. 54

CHAPTER 5 - CONCLUSIONS AND FUTURE WORK............................................... 63

REFERENCES.................................................................................................................. 66

VITA


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LIST OF FIGURES

Fig. 3.1 PSD of noise recorded in an aircraft cockpit. ..................................................... 28

Fig. 3.2 PSD of noise recorded in a destroyer engine room............................................. 28

Fig. 3.3 PSD of input noise signal and residual error signal. ........................................... 30

Fig. 3.4 MSE of feedback FXLMS algorithm for white noise......................................... 31

Fig. 3.6 MSE of secondary path estimate as a function of filter length. ......................... 34

Fig. 3.7 Estimate of Secondary Path Transfer function. ................................................. 35

Fig. 3.8 MSE plot for the feedback LMS and feedback NLMS algorithms for a 150Hz.

sine wave ................................................................................................................... 37

Fig. 3.9 MSE plot for colored noise at 125Hz. ............................................................... 38

Fig. 3.10 MSE plot for colored noise at 750Hz. ............................................................... 39

Fig. 4.1 Magnitude response of 1000Hz low pass filter................................................. 46

Fig. 4.2 Magnitude response of 1000Hz high pass filter. ............................................... 46

Fig. 4.3 PSD and time plots for sine waves at 30Hz. ...................................................... 49

Fig. 4.4 MSE plot for sine waves at 30Hz. ..................................................................... 49

Fig. 4.5 PSD of input noise and time plots for sine waves at 300Hz and 2000Hz. ........ 50

Fig. 4.6 MSE plots for sine waves at 300Hz and 2000Hz. ............................................. 51

Fig. 4.7 PSD of input noise and time plots for sine waves at 600Hz and 2500Hz. ........ 51

Fig. 4.8 MSE plot for sine waves at 600Hz and 2500Hz. ............................................... 52

Fig. 4.9 PSD of input noise and time plots for sine waves at 4000Hz............................ 53

Fig. 4.10 MSE plot of sine waves at 4000Hz.................................................................... 53

Fig. 4.11 4th order bandpass IIR filter with a 250Hz-500Hz passband. ........................... 54Fig. 4.12 4th order bandpass IIR filter with a passband of 1250Hz-1500Hz.................... 55

Fig. 4.13 PSD of input noise and time plots for colored noise with 125Hz centre

frequency. .................................................................................................................. 56

Fig. 4.14 MSE plot for colored noise with 125Hz centre frequency. ............................... 57

Fig. 4.15 PSD of primary noise and time plots for noise at 500Hz and 1500Hz. ............. 58


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Fig. 4.16 MSE plots for noise at 500HZ and 1500Hz....................................................... 58

Fig. 4.17 PSD of primary noise and time plots for noise at 750Hz and 2000Hz. ............. 59

Fig. 4.18 MSE plot for noise at 750Hz and 2000Hz. ........................................................ 59

Fig. 4.19 PSD of primary noise and time plots for noise at 3000Hz. ............................... 60Fig. 4.20 MSE plots for noise at 3000Hz.......................................................................... 61


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1

CHAPTER 1

INTRODUCTION

Acoustic problems in the environment have gained attention due to the tremendous

growth of technology that has led to 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

problem of controlling the noise level in the environment has been the focus of a

tremendous amount of research over the years.

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

performance of these systems is also limited to a fixed structure and proves impractical in

a number of situations where space is at a premium and the added bulk can be a

hindrance. The shortcomings of the passive noise reduction methods have given impetus

to the research and applications of alternate methods of controlling noise in the

environment.Various signal processing techniques have been proposed over the years for noise

reduction in the environment. The explosive growth of digital processing algorithms and

technologies has given an impetus to the application of these techniques to the real world.


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Digital Signal Processors (DSPs) have shrunk tremendously in size while their processing

capabilities have grown exponentially. At the same time the power consumption of these

DSPs has steadily decreased following the path laid down by Genes law. This has

enabled the use of DSPs in a variety of portable hearing enhancement devices such as

hearing aids, headsets, hearing protectors, etc.

There are two different approaches for electrical noise reduction. The first

approach is passive electrical noise reduction techniques, such as those applied in hearing

aids, cochlear implants, etc. where the signal and ambient noise are recorded using a

microphone, noise reduction techniques such as spectral subtraction, the LMS algorithm,

etc are applied and the listener hears only the clean signal. One of the important

assumptions of this technique is that the listener is acoustically isolated from the

environment. This assumption is however not valid in a large number of situations

particularly those where the ambient noise has a very large amplitude. In such situations,

the second approach of Active Noise Cancellation (ANC) is applicable. ANC refers to an

electromechanical or electroacoustic technique of canceling acoustic disturbance to yield

a quieter environment. The basic principle of ANC is to introduce a canceling antinoise

signal that has the same amplitude but the exact opposite phase, thus resulting in an

attenuated residual noise signal. ANC has been used in a number of applications such as

hearing protectors, headsets, etc.

The traditional 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. Most noise sources tend to be broadband in nature and while a large


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portion of the energy is concentrated in the lower frequencies, they also tend to have

significant high frequency components. Further, as the ANC system is combined with

other communication and sound systems, it is necessary to have a frequency dependent

noise cancellation system to avoid adversely affecting the desired signal.

To account for the possibility that the noise might reside in disjoint frequency

bands, this thesis proposes a subband approach to feedback ANC. The applications

considered in this thesis are headsets, hearing protectors and other assistive hearing

devices. Chapter 2 reviews the various ANC techniques that have been developed,

Chapter 3 discusses the development and implementation of the proposed subband ANC

technique, the result of the aforementioned system are discussed in Chapter 4 and

Chapter 5 presents a summary of the work done as well as suggestions for further

avenues of research.


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Fig. 2.1. Physical concept of Active Noise Control.

CHAPTER 2

LITERATURE SURVEY

Acoustic Noise Control traditionally involves passive methods such as enclosures,

barriers and silencers to attenuate noise. These techniques use either the concept of

impendence change or the energy loss due to sound absorbing materials. These methods

are however not effective for low frequency noise. A 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 as shown in Figure 2.1.

Primary NoiseWaveform

Secondary NoiseWaveform (antinoise)

Residual Noise

Waveform


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The design of ANC systems was first conceived in the 1930s by Lueg [1]. In the ensuing

years, ANC has been the focus of a lot of research. An overview can be found in the

tutorial paper by Kuo and Morgan [2] and also in the book by the same authors [3].

ANC systems are based either on feedforward control where a coherent reference noise

input is sensed or feedback control [5] where the controller does not have the benefit of a

reference signal. Further, ANC systems are classified based on the type of noise they

attempt to cancel as either broadband or narrowband. A brief overview of the various

approaches to ANC follows next.

2.1 Broadband feedforward Active Noise Control

These are systems that have a single secondary source, a single reference sensor and a

single error sensor. The single channel duct acoustic ANC system shown in Figure 2.2 is

an example of such a system

Primary noiseoise

ANC

Reference mic

Cancelingloudspeaker

Error mic

Fig. 2.2. Single channel broadband feedforward Active Noise Control.

Cancelingantinoise


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This basic broadband ANC system can be described as an adaptive system identification

framework as shown in Figure 2.3. Essentially, an adaptive filter W(z) is used to estimate

an unknown plant P(z) which consists of the acoustic response from the reference sensor

to the error sensor. The objective of the adaptive filter W(z) is to minimize the residual

error signal e(n). However, the main difference from the traditional system identification

scheme is the use of an acoustic summing junction instead of the subtraction of electrical

signals. Therefore it is necessary to compensate for the secondary path transfer function

S(z) from the output of the adaptive filter till the point where the error signal gets

recorded.

From Figure 2.3, we see that the z transform of the error signal is given by

[ ])()()()()( zW zS zP z X z E = 2.1

Assuming that after convergence of the adaptive filter, the error signal is zero, W(z) is

required to realize the optimal transfer function

P(z)

W(z) S(z)

LMS

x n)

x n

y(n)

d n) e n)+

-

y(n)

Fig. 2.3. System identification view of ANC.


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)()(

)( zS zP

zW = 2.2

The introduction of the secondary path transfer function in a system using the standard

LMS algorithm leads to instability. This is because, it is impossible to compensate for the

inherent delay due to S(z) if the primary path P(z) does not contain a delay of equal

length. Also, a very large FIR filter would be required to effectively model 1/S(z). This

can be solved by placing an identical filter in the reference signal path to the weight

update of the LMS equation. This is known as the filtered-X LMS algorithm [5] [6]. The

block diagram of an ANC system using the FXLMS algorithm is shown in Figure 2.4.

A rudimentary explanation of the FXLMS algorithm is presented below.

In figure 2.4, the residual error signal can be expressed as

P(z)

W(z) S(z)

S^(z)

LMS

x(n)

x(n)

y(n)

d(n)

e(n)

-

Fig. 2.4. ANC system using the FXLMS algorithm.


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E(n) = d(n) s(n)*[ wT(n)x(n)] 2.3

where s(n) is the impulse response of the secondary path S(z) at time n. Assuming a mean

square cost function (n) = E[e 2(n)], the adaptive filter minimizes the instantaneous

squared error )( n = e 2(n) according to

)(2

)()1( nnn =+ ww 2.4

since

)()('2)( nenn x= 2.5

the weight update equation reduces to

)()(')()1( nennn xww +=+ 2.6

In practical applications, the secondary path transfer function S(z) is unknown and must

be estimated by an additional filter )( zS . Therefore, x(n) = )( nS * x(n), where )( nS is

the impulse response of )( zS . As shown by Morgan [7], the FXLMS algorithm seems to

be remarkably tolerant to errors in the estimation of S(z) by the filter ) ( zS and within the

limit of slow adaptation, the algorithm will converge with nearly 90 of phase error

between )( zS and S(z) [7]. Therefore, offline modeling techniques can be used to model

S(z) [3]. Nelson and Elliot [8] showed that the maximum step size that can be used with

the FXLMS algorithm is given by

)('1

max+

= LP x

2.7

where P x = E[x 2(n)] is the power of the filtered reference signal and is the number of

samples corresponding to the overall delay in the secondary path. However, errors in


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estimating the secondary path transfer function will alter the stability bounds on [9]. A

detailed analysis of the stability criterion is available in the literature[10]

In the feedforward ANC system shown in Figure 2.3, the antinoise output of the

speaker also radiates upstream to the reference microphone resulting in acoustic feedback

and hence a corrupted reference signal x(n). Instability will occur if the open loop phase

lag reaches 180 and the gain is greater than unity. This can be solved by using a separate

offline adaptive feedback cancellation filter within the ANC system. Feedback can also

be solved by using an adaptive IIR filter in place of the FIR filter in the ANC system.

However, IIR filters are not unconditionally stable, as adaptation may converge to a local

minimum and can have relatively slow convergence rates. A detailed analysis of adaptive

IIR filters is available in the literature [11].

2.2 Narrowband Feedforward ANC

Many noise sources are periodic in nature such as engines, compressors, motors, fans,

etc. In such cases, direct observation of the mechanical motion using an appropriate

sensor is used to provide an electrical reference signal which consists of the primary

frequency and all the harmonics of the generated noise. The basic block diagram is as

shown in Figure 2.5


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This technique avoids the undesired acoustic feedback to the reference sensor, as well as

nonlinearities and aging problems with acoustic microphones. The periodicity of the

noise removes the causality constraint, as each harmonic can be controlled independently

and a much shorter FIR filter can be used to model the secondary path.

There are two techniques for narrowband ANC i.e. the waveform synthesis

method, which uses an impulse train with a period equal to the inverse of the fundamental

frequency of the disturbance. The second technique uses an adaptive notch filter with a

sinusoidal reference signal.

2.3 Feedback Active Noise Control

Feedforward ANC systems (broadband and narrowband) use a reference sensor to

measure the primary noise signal, a feedforward adaptive filter and an error sensor to

measure the residual error signal. However, in some applications, it is not feasible to have

Primary noise Noise

Source


Error mic

Digital filter

LMS

SignalGenerator

x n) n)

Nonacousticsensor

Fig. 2.5. Narrowband feedforward ANC system.


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In Figure 2.6 above, d(n) is the primary noise at the error sensor location, e(n) is the

residual noise, y(n) is the secondary antinoise signal, W(z) is the transfer function of the

controller and S(z) is the transfer function of the secondary path. Under steady state

conditions, the z-transform of the error signal can be expressed as

)()()()()( z E zW zS z D z E =

)()(1)(

)( zW zS

z D z E

+=

2.8

2.9

Therefore the closed loop transfer function H(z) from the primary noise to the error signal

can be expressed as

)()(11

)()(

)( zW zS z D

z E z H

+== 2.10

From equation 2.9 the power spectrum of the error signal is given by

)()()(1

1)( 2 wS

wW wS wS dd ee

+= 2.11

W(z) S(z)

d(n)

y(n)

d(n)

e(n)

-

H(z)

Fig. 2.6. Classical feedback ANC system.


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where S ee(w) and S dd(w) are the power spectra of the error signal e(n) and the reference

noise d(n) respectively. Therefore, in order to minimize S ee(w), we need to minimize

2)()(1 zW zS + , or the gain of S(z)W(z) should approach infinity. If the frequency

response of S(w) is flat, then the gain of W(w) can be increased without limit so that the

overall transfer function of the feedback loop becomes marginal. However, this is rarely

the case as the response of the secondary source introduces a significant phase shift and

there is some propagation delay from the output of the control filter to the error sensor.

These effects introduce a phase shift in S(w) that increases with frequency. As the phase

shift approaches 180 , the desired negative feedback becomes positive feedback leading

to instability. Therefore as the frequency and phase shift increase, the gain of W(w)

should decrease. Hence it is possible to design an inverting amplifier W(w) provided the

gain is not large enough to make the net loop gain greater than unity when the phase shift

is 180 . Therefore, if

)()()()( w jewGwW wS =

)(cos)(2)(1)()(1 22

wwGwGwW wS ++=+

2.12

2.13

Given a secondary path S(w), W(w) needs to be chosen such that the net gain G(w) is

maximized when -180 < (w) < 180 . A more detailed explanation of the design of

feedback ANC system is available in the literature [3][13][14].

Single channel Adaptive Feedback Active Noise Cancellation

The adaptive single channel Active Noise Cancellation system was first proposed by

Eriksson[16] and then extended to the multi channel scenario by Popovich [17][18]. This


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technique is generally viewed as an adaptive feedforward ANC system that in effect

synthesizes its own reference signal. Under certain conditions, the system can also be

interpreted as an adaptive predictor[19].

In the feedback ANC system shown in Figure 2.6, the primary noise signal d(n) is

not available. Therefore, the main idea of an adaptive feedback ANC system is to

regenerate the reference signal d(n) from the error signal. From Fig 2.6, we can see that

the primary noise can be expressed in the z-domain as

)()()()( zY zS z E z D += 2.14

where E(z) is the residual error signal obtained from the error signal and Y(z) is the

output of the adaptive filter. The secondary path transfer function S(z) can also be

estimated as )( zS . Thus we can estimate the primary noise d(n) and use this as a

synthesized reference signal x(n) as follows

)()()()()( zY zS z E z D z X += 2.15

This is illustrated in Figure 2.7

W(z) S(z)

d(n)

y(n)

x(n)

e(n)

-

S(z)

+

Fig. 2.7. Adaptive feedback ANC system using synthesized reference signal.


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A complete block diagram of the broadband ANC system is shown in Figure 2.8

From Figure 2.8, we can see that the reference signal x(n) which is synthesized from the

error signal can be expressed as

=+=

1

0

)()()()( M

mm mn ysnend n x 2.16

where ms , m = 0, 1, .M-1 is the Mth order FIR filter ( )( zS ) used to approximate

the secondary path transfer function. This estimation can be performed either online or

offline. The secondary signal y(n) is generated as

==

1

0

)()()( L

ll ln xnwn y 2.17

S^(z)

W(z) S(z)

LMS

S^(z)

x(n)

x(n)

y(n)

d(n)

d^(n)

e(n)+

+

+

-y1(n)

y1(n)

Fig. 2.8. Broadband feedback Active Noise Cancellation using the FXLMS algorithm.


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where w l(n), l = 0, 1, L-1 are the coefficients of the Lth order adaptive FIR filter

W(z) at time n. These coefficients are updated by the FXLMS algorithm as

)()(')()1( leln xnwnw ll +=+ 2.18

where is the step size and the filtered reference signal x(n) is given by

=

1

0

^

)()(' M

m

m mn xsn x 2.19

From equations 2.14 and 2.15, we can see that x(n) = d(n) if )( zS = S(z). Assuming that

this condition is satisfied, then the adaptive feedback ANC system in Fig 2.8 can be

transformed into the feedforward ANC system in Figure 2.4. The adaptive filter W(z) can

be commuted with the secondary path transfer function S(z) if the LMS algorithm has

slow convergence, i.e. the step size is small [5]. Further, if we assume that the

secondary path S(z) can be modeled as a pure delay i.e. S(z) = z -, then the feedback

ANC system is equivalent to the standard adaptive predictor as shown in Figure 2.9.

W(z)

LMS

z-

x(n)

d(n)

e(n)+

-

Fig. 2.9. Feedback Active Noise Cancellation algorithm asan adaptive predictor.


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Thus the feedback ANC algorithm acts as an adaptive predictor of the primary noise d(n)

to minimize the residual error noise e(n). Hence the performance of the algorithm

depends on the predictability of the primary noise d(n). A detailed analysis of the

feedback ANC algorithm as an adaptive predictor is available in the literature[19].

We know that the error signal in Figure 2.8 can be expressed in the z-domain as

)()()()( zY zS z D z E = 2.20

where

)()()( z X zW zY =

)]()()()[()( zY zS z E xW zY +=

2.21

2.22

Rearranging equation 2.22 we get

)()()()]()(1[ z E zW zY zW zS =

)()(1

)()()( zW zS

z E zW zY =

2.23

2.24

Substituting equation 2.24 in 2.20, we get

=

)()(1

)()()()()(

zW zS

z E zW zS z D z E

)()()()(1

)()(1 z D z E zW zS

zW zS =+

+

=

)()(1

)()(1

)()(

zW zS

zW zS

z D z E

2.25

2.26

2.27


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)()]()([1

)()(1)()(

^

zW zS zS

zW zS z D z E

+

= 2.28

Assuming )( zS = S(z), equation 2.28 simplifies to

)()()()()( z D zW zS z D z E = 2.29

Therefore, the overall transfer function of the feedback ANC system from d(n) to e(n) is

given by

)()(1)()(

)( zW zS z D z E

z H == 2.30

Therefore under ideal conditions, the feedback ANC system is transformed to a

feedforward ANC system.

For certain applications where the noise to be cancelled is narrowband, the

waveform synthesis method can be used. In this method, the regenerated reference signal

x(n) is used to synthesize a low frequency component that has a repetition rate locked to

the fundamental driving frequency of the primary noise source. The reference signal

estimate is fed directly to a phased lock loop, which generates a synchronization pulse for

a waveform synthesizer. A more detailed explanation is available in the literature [20].

A number of alternate schemes have been proposed for feedback ANC. Oppenheim and

Zangi [21] proposed a feedback ANC scheme based on the block Expectation Maximize

algorithm. Openheim et al [22] proposed a scheme based on the RLS algorithm.

However, these algorithms have been generated with ideal conditions and initial

conditions need to be very carefully generated to ensure that the algorithm converges.

Eriksson et al [23] proposed a generalized recursive ANC scheme that uses three adaptive


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filters that accurately model the primary path, the feedforward path and the feedback path

for the filtered X or filtered U algorithms. Performance analysis of all these algorithms

have shown that the noise attenuation is very noticeable in the lower frequency regions

below 1kHz and deteriorates very rapidly as the center frequency of the noise increases

[3][19][24].

Hybrid Active Noise Control systems

A combination of the feedforward and feedback ANC schemes is known as the Hybrid

ANC scheme. Here, the canceling signal is generated based on the inputs of both the

reference sensor and the error sensor. This method was first proposed by Swanson [27].

The motivation behind this method is to increase the correlation between the primary

noise and the signal picked up by the reference sensor. Since the error sensor is generally

placed downstream from the source of the primary noise and the reference sensor is

places as close as possible to the primary source. However, it is often the case that the

reference sensor may not pick up all the acoustic cues of the primary noise source and

this can be rectified by using the signal at the error sensor also to generate the canceling

output [19]. The block diagram of the Hybrid ANC scheme is as shown in Figure 2.10


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The system in Figure 2.10 can be configured with the feedforward path as any one of the

following:

1. Filtered-X LMS algorithm

2. Filtered-X LMS algorithm with feedback cancellation

3. Filtered-U recursive LMS algorithm

The feedback path can be configured to be

1. Classical feedback ANC

2. Feedback ANC using Filtered-X LMS algorithm

3. Output whitening method [28]

The canceling signal fed to the speaker is generally an unweighted sum of the outputs of

both algorithms. Vijayan [19] showed that the hybrid scheme was better at canceling

broadband noise, when compared to the feedforward or feedback schemes by themselves.

Primar noise NoiseSource

Reference mic


Error mic

Feedback

ANCFeedforward

ANC

Fig. 2.10. Active Noise Cancellation system with both feedback and feedforward control loops.


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Furthermore, she showed that it is possible to reduce the length of the filters in the hybrid

scheme.

Feedback Active Noise Cancellation has been used in many applications. It has

been used in hearing protectors such as headsets[13][14][15][24] along with other passive

methods to reduce noise especially on the factory floor and in aircraft cockpits, etc. There

are many commercially available products that use nonadaptive ANC schemes for noise

cancellation in headsets. ANC has also been combined with other applications such as

headsets for communication purposes [24], in integrated hands-free kits for cellular

phones [25] and has been implemented using the speaker and microphone available in the

cellular phone itself [26]. In all these applications, the generated antinoise needs to be

combined with the signal of interest such as the received speech signal or the audio signal

from an external sound source, etc. Hence the error microphone will pick up the residual

error source but also the signal from the external source. Therefore, it is possible that the

antinoise signal generated by the ANC system can degrade the quality of the desired

signal as well.

2.3 Multi channel Active Noise Cancellation

In many applications, it is desirable to cancel noise at several locations in a three

dimensional space. Single channel systems are effective when the area of interest is

restricted and there is only a single primary source that can be accurately located and a

single quiet zone where the error sensor needs to be located. However, many practical

applications involve relatively large multidimensional spaces where the noise source

cannot be accurately pointed to be at one single location. The complexity of multi


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channel ANC in a multi dimensional space is however significantly higher and the

system needs to be carefully ported to a practical real world application.

The best known applications of multichannel systems are in the control of

exhaust noise in automobile cabins as well as in the cabins of heavy equipment such as

earth movers, flight cabins, etc [29][30]. These algorithms generally tend to be single

reference, multiple error sensors. The idea is to use a single nonacoustic sensor to

generate the periodic reference signal and to minimize the sum of the squares of the

outputs of a large number of equally spaced error sensors. Generally, multi channel

algorithms are necessary when the area in which ANC needs to be performed becomes

larger. Elliott[31] proposed a multi channel FXLMS algorithm to cancel the noise

created by rotating machinery using multiple error sensors and a single nonacoustic

reference sensor. Signal processing structures have also been proposed for multiple

reference, multiple output broadband feedforward ANC[32]. Multichannel ANC usually

requires careful research into the acoustic characteristics of the environment in which it is

being implemented. Usually, the secondary path transfer functions have a nonminimum

phase, i.e. have zeros outside the unit circle due to the reverberances in the three

dimensional space. The general strategy is to minimize the total energy in the

multidimensional space i.e. the sum of the outputs of all the error sensors. Therefore, the

location of these sensors is very important so that it represents the sum total of the energy

in the multidimensional space.

The multichannel feedforward ANC system can thus be viewed to be a

combination of single channel feedforward systems, with the exception that there are

multiple secondary paths from each of the adaptive filters to each of the error sensors.


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Multichannel feedforward algorithms are also generally prone to feedback due to the

larger number of error and reference sensors. It has also generally been found that IIR

adaptive filters are more effective than FIR filters in multi channel systems [33]. Multi

channel systems have also been implemented using the feedback ANC algorithm using

either a K X 1 system with K reference sources and a single error source or a K X M

system with K reference sensors and M error sensors [3].

2.4 Frequency Domain and Subband Active Noise Cancellation

Frequency domain ANC:

The feedforward ANC system has also been implemented in the frequency domain. In

this implementation, the reference signal x(n) is first stored in a L point buffer and then

transformed into the frequency domain signal using an L point FFT. The FFT spectrum is

then multiplied by the appropriate adaptive weights to generate a frequency domain

output signal which is then retransformed into the time domain using an L point IFFT.

This is as shown in Figure 2.11.


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The system shown in Figure 2.11 was first proposed by Shen and Spanias [34] and

subsequently extended to the multiple channel case [35]. Reichard and Swanson [36]

implemented a frequency domain feedforward FXLMS structure with online system

identification. Feintuch et al [37] showed that as long as the frequency band of interest

was limited, it was not really necessary to estimate the transfer function of the secondary

path before adaptation and it was only necessary to know the delay introduced by the

transfer function in the band. The major drawback of the frequency domain algorithm is

that it processes the data block by block instead of sample by sample. Thus there are L

samples of delay between the input of the reference signal and the output of the

secondary antinoise signal. This delay would be tolerable for very low frequency periodic

noise. However, in the case of broadband noise , the delay is a major shortcoming. The

P(z)

W(z) S(z)

S^(z)

LMS

x(n)

x n

y(n)

d(n)

e(n)

-FFT

FFT

FFT

IFFT

Fig. 2.11. Frequency domain feedback FXLMS algorithm.


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delay caused when the frequency domain FXLMS algorithm is adapted to the feedback

ANC system becomes 2L as there is a further L sample delay while the reference signal is

regenerated. Hence the frequency domain implementation of the feedback FXLMS

structure is highly inappropriate.

Subband Active Noise Cancellation:

There are a number of applications in which ANC has been used to cancel broadband

noise. In order to effectively cancel broadband noise, it is essential that adaptive filters

with hundreds of taps be used. However, these are not only computationally intensive,

but also display very slow convergence. Moreover, ANC has also been used in

conjunction with other applications. In this scenario where the speaker is used not only to

play the antinoise signal but also a desired signal from a secondary source, the error

sensor will pick up both the residual noise as well as the desired signal. Hence it is

probable that the generated antinoise signal will degrade the quality of the desired signal

as well. Subband adaptive filtering techniques have previously been proposed to solve

the problems for acoustic echo cancellation, signal enhancement, etc. [38]. Morgan and

Thi [39] adapted the same idea for feedforward Active Noise Control. The proposed

structure was very similar to the frequency domain structure proposed earlier, i.e. the

adaptive weights are computed for each subband (FFT bin) separately, and then

transmitted to an equivalent wideband filter. However, it differs from the frequency

domain structure in that the actual processing of the subband signal takes place in the

time domain. This technique is computationally intensive as it is required to take a

polyphase FFT of both the error and filtered reference signals as well as an inverse FFT


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of the filter weights. It is still less intensive than an equivalent wideband adaptive filter

[40]. Park et al [41] proposed a modification to the subband adaptive filter architecture

that decomposed the secondary path transfer function into a series of subbands as well.

Both these studies showed that the subband technique had a significantly better

convergence when compared with the traditional wideband FXLMS algorithm. The

subband technique is all the more important when ANC is used in conjunction with

another application. Hussain and Campbell [42] studied the application of subband ANC

to speech that had been corrupted with automobile noise. Their technique used two

separate channels, with the subband technique applied separately on each channel. These

subband techniques however, do not translate well to the feedback FXLMS system due to

the need to buffer the reference signal and the error signal.

A number of techniques have been proposed for subband adaptive filtering using

filterbanks. Vitterli and Gilloire [43] and Usevitch and Orchard [44] separately proposed

a subband filtering scheme where the expected signal and the error signal were divided

into subbands using a filterbank and each subband was then processed independently.

The conditions for the filterbank were researched by Petraglia and Alves [45] . Alves et al

[46] studied the convergence properties of the subband adaptive filter structure. The

filterbank method is more suitable for subband feedback ANC as the processing can be

done on a per sample basis. The next chapter presents the proposed subband feedback

Active Noise Cancellation system.


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CHAPTER 3

PROPOSED SUBBAND ACTIVE NOISE CANCELLATION ALGORITHM

We have seen in the previous chapter that the traditional 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. Further, as the ANC system is

combined with other communication and sound systems, it is necessary to have a

frequency dependent noise cancellation system to avoid adversely affecting the desired

signal. This chapter discusses such a subband feedback active noise cancellation system

and its application to headsets.

3.1 Motivation

Traditional Active Noise Cancellation systems are most effective for low frequency

periodic 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. 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.

Figures 3.1 and 3.2 illustrate the psd of different kinds of noise.


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Fig. 3.1. PSD of noise recorded in an aircraft cockpit.

Fig. 3.2. PSD of noise recorded in a destroyer engine room.


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Experiments were performed to quantify the performance of feedback Active Noise

Cancellation systems as the frequency of the primary noise source increased using a

commercially available Bose QuietComfort ANC headset. The headset uses a

nonadaptive analog system for ANC. A Knowles Electronic Manikin for Acoustic

Research (KEMAR) was placed in a sound booth and the 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

energy of the noise in dB SPL is shown in Table 3.1

Frequency ofbroadband

noise

Noise level with theheadset on and ANCturned off (dB SPL)

Noise level withheadset on and ANCturned on (dB SPL)

250 Hz 80 65

500 Hz 70 70750 Hz 70 751000 Hz 68 722000 Hz 75 753000 Hz 70 704000 Hz 62 62

Table 3.1. Noise attenuation of the Bose ANC headsets at different frequencies.

This experiment indicated that the performance of the analog feedback ANC system

deteriorated rapidly as the interference frequency increased. At frequencies of 500Hz and

above, the ANC system provided no attenuation and it was found that at certain

frequencies, the ANC system actually had a detrimental effect.


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The problem of wideband ANC can be solved to some extent by using an adaptive

feedback ANC system. However, wideband adaptive ANC techniques require long

adaptive filters with hundreds of taps for effective noise cancellation. The filters are not

only computationally very intensive, but also suffer from slow convergence. Figures 3.3

and 3.4 show the simulated performance of an adaptive ANC system for white noise. The

input white noise was generated using MATLAB and was run through the feedback

FXLMS algorithm with a 20 tap adaptive filter. Figure 3.3 plots the learning curve of the

system and Figure 3.4 plots the psd of the input noise signal and the psd of the error

signal.

Fig. 3.3. PSD of input noise signal and residual error signal.


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Fig. 3.4. MSE of feedback FXLMS algorithm for white noise.

We can see from Figures 3.3 and 3.4 that the feedback FXLMS algorithm does not

converge and hence there is little or no noise attenuation.

Further, as the ANC system is combined with other applications such as cellular

phones, in-car sound systems, hand free kits, etc. it becomes imperative that the ANC

system preserves the quality of the desired signal.

Many new techniques have been proposed based on subband adaptive filtering

[43] [44] [45] [46] to reduce the computational complexity and convergence speed.

Morgan [7] studied the application of these techniques to feedforward active noise

control and concluded that the delay introduced into the auxiliary path due to the


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presence of the bandpass filter significantly reduced the bandwidth of the system. An

alternate delayless subband Active Noise Control system was proposed [40][41] in which

the subband filter weight update was done in the transform domain and then transferred

to a time domain adaptive filter. However, the proposed techniques do not translate very

well to the feedback ANC system in which the reference signal is regenerated from the

error signal. The feedback FXLMS algorithm 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. Also the proposed filterbank approach to subband filtering

provides significant computational advantages over the existing methods for feedforward

subband ANC. Since ANC headset systems will tend to be battery powered and therefore

will be implemented on fixed point DSP systems, this directly leads to savings in MIPS

required to implement the system and hence the power requirements.

The following sections describe the proposed subband feedback Active Noise

Cancellation. Section 3.2 describes the procedure that was followed to estimate the

secondary path transfer function, Section 3.3 describes the NLMS algorithm that was

used and Section 3.4 describes the subband ANC system.

3.2 Secondary Path Modeling

The FXLMS algorithm requires knowledge of the secondary path transfer function S(z).

Assuming the transfer function is linear and time invariant, an offline modeling technique


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can be used to estimate the transfer function during an initial training stage. The estimate

of the transfer function )( zS at the end of the training period was used. The experiments

were carried out using a pair of NCT headphones, which had a microphone acting as the

error sensor in each earpiece. The signal processing was carried out on a DHP 100 EVM

an EVM based on the TMS320C5402 DSP with an AIC 23 stereo codec [48]. The LMS

algorithm was implemented in fixed point C using varying number of filter taps to

identify the system. White noise was used as the training signal. The system used to

estimate the secondary path transfer function was as shown in Figure 3.5.

S^(z)

LMS

x n

n e n-

White noiseenerator

D/A

Low PassFilter

Power Am lifier

A/D

Anti aliasingfilter

Pre-amplifier

d n

Louds eaker Error micro hone

S z)

DSPS stem

Fig. 3.5. Experimental setup for offline secondary path modeling.


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The experiment was run using adaptive filters with 5 taps through 25 taps in length to

determine the optimum number of taps. Figure 3.6 shows the mean squared error as a

function of the filter length.

Fig. 3.6. MSE of secondary path estimate as a function of filter length.

A filter length of 20 was used for the simulations. The estimate was tried with a number

of people from the Speech Processing Research Laboratory at the University of Texas at

Dallas and an average profile was used. The estimate of the transfer function is shown in

Figure 3.7 below.


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Fig. 3.7. Estimate of Secondary Path Transfer function.

3.3 Filtered X-LMS algorithm

The feedback FXLMS algorithm serves as the basic block for the proposed subband

Active Noise Cancellation system as well as serving as a comparative algorithm. The

basic feedback FXLMS algorithm, as described in the literature [2] [3] [16] [19], was

implemented in MATLAB. A simple Least Mean Square algorithm was used with a small

step size in the order of 0.0005. The estimated secondary path transfer function ) ( zS was

used for both the true secondary path transfer function S(z) as well as the estimate. Ideal

conditions were assumed implicitly in that there was no error in the estimation of the


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secondary path. The advantages of using the normalized LMS algorithm are well

documented [5] for faster convergence and a lower mean squared error. 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 than the LMS algorithm. The step

size of the adaptive filter was calculated as

+=

P p L

i

3.1

where p i 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 p i was calculated as the magnitude squared of the

input signal. The power p i was also estimated using the Teager energy operator [48] [49],

which is based on a definition of energy that accounts for the energy in the system that

generated the signal. The Teager energy operator estimates the instantaneous power of a

discrete time signal according to

]1[]1[][])[( 2 += n xn xn xn xd 3.2

The performance improvement in using the Teager energy operator was not found to be

significant and given the extra complexity in using the Teager operator, the conventional

method of estimating the energy was used.

Figure 3.8 plots the MSE for the feedback FXLMS and the feedback FX-NLMS

algorithms for a 150 Hz sine wave.


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Fig. 3.8. MSE plot for the feedback LMS and feedback NLMS algorithms for a 150Hz.

sine wave

To further validate the system, the simulations were carried out using pink noise with

different center frequencies as an input. The input was generated by passing white noise

generated using the MATLAB rand command through bandpass filters with a fixed

bandwidth of 250Hz and different center frequencies. Figure 3.9 and 3.10 show the MSE

of the LMS and NLMS systems for colored noise at 125Hz and 750Hz respectively.


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Fig. 3.9. MSE plot for colored noise at 125Hz.


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Fig. 3.10. MSE plot for colored noise at 750Hz.

We can see from Figures 3.9 and 3.10 that the NLMS algorithm had better convergencerate and lowered the MSE of the residual error signal.

Simulations were also carried out to determine the optimal length of the adaptive

filter, for the feedback FXNLMS algorithm, with different filter lengths and for colored

noise at a range of frequencies. 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 developed in the next section.


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3.4 Proposed Subband Active Noise Cancellation System

This section describes the proposed subband Active Noise Cancellation system. The basic

idea has been adopted from filterbank-based subband adaptive processing techniques for

various applications, to the feedback ANC system. The residual error signal recorded is

split into a number of bands using linear phase bandpass FIR filters and the FXNLMS

algorithm described in the previous section 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. The block diagram of the system is shown in Figure 3.11


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We can see from Figure 3.11 that an additional delay is introduced into the secondary

path due to the presence of the bandpass filter in each of the subbands. For the feedback

ANC system to converge, the delay introduced in the secondary path needs to be

compensated for. This is done by using the same filter along with the secondary path

estimate as the input for the LMS update equation. An example of such a system using

two discreet frequency bands is illustrated in Figure 3.12

S(z)

d n

e n+

FIR 1

FIR n

+

Feedback ANC band n

Feedback ANC band 1

+

Fig. 3.11. The proposed Subband feedback Active Noise Cancellation System.


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Fig. 3.12. Proposed subband feedback ANC system with two bands.

Feedback FXNLMS algorithm

S(z)

d(n)

e(n)

+

-

y1(n)

S^(z)

W1(z)

LMS

S^(z)

x1(n)

x1(n)

d1^(n)+

+

y1(n)

H1(z)

H1(z)

S^(z)

W2(z)

LMS

S^(z)

x2(n)

x2(n)

y(n)

d2^(n)+

+

y2(n)

H2(z)

H2(z)

+

+


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We can see from Figure 3.12 that there is an additional source of delay introduced due to

the bandpass filter H 1(z). The delay introduced by the presence of this filter is

compensated by introducing the same filter H 1(z) in sequence with the secondary path

estimate )( zS to the LMS update equation. The subband feedback FXLMS system shown

in Figure 3.12 is cascaded as shown in Figure 3.11 so that the ANC system covers the

entire spectrum of interest.

A number of techniques were tested for the n th bandpass filter H n(z) used to filter

the residual error signal. The system was first tested using butterworth IIR filters to do

the bandpass filtering. However, it was found that the delay introduced by the IIR filters

was too large for the system to converge. Also, the system was found to be highly

unstable. The system was then tested using FIR filters of varying length. The system was

found to perform best with 20 tap 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 frequencies and bandpass filters with a bandwidth of 500-1000Hz. The simplest

system used included two distinct bands, one for noise below 1kHz and another 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


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noise attenuation up to 4kHz. The tradeoff to the increased bandwidth led to 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 results of the subband feedback ANC system are presented next in Chapter

4 for a wide range of input signals.


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CHAPTER 4

RESULTS

This chapter evaluates the performance of the subband feedback ANC system proposed

in Chapter 3. A two band system was implemented in MATLAB and simulations were

carried out using a wide variety of simulated inputs. The simulations were carried out

with two distinct frequency bands one band for signals below 1kHz and the other band

for signals above 1kHz. A sampling frequency of at least 8kHz was used. The error signal

was split into subbands using 20 tap linear phase FIR filters with 30dB of attenuation in

the stop band designed using MATLABs Filter Design Toolbox.

Figure 4.1 shows the frequency response of the low pass FIR filter and Figure 4.2 shows

the magnitude response of the high pass FIR filter.


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Fig. 4.1. Frequency response of 1000Hz low pass filter.

Fig. 4.2. Frequency response of 1000Hz high pass filter.


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Simulations were run using a number of different input files to evaluate the stability and

the performance of the system. The simulations were carried out using sine waves and

artificially generated colored noise at different frequencies. The subband method was

compared with the classical feedback FXLMS algorithm as described in [3]. The

performance of the system was evaluated using Mean Squared Error (MSE) plots as

described by Widrow and Stearns [5] and by calculating the improvement in the noise

attenuation obtained. A visual inspection of the time plots of the residual error signals

was also a good measure of evaluating the relative performance. It must be noted that the

convergence times of all ANC systems was kept artificially long by using very small

values for the LMS adaptation constant . This was done so as to cancel out only the

steady state noise and not adversely affect the quality of the desirable ambient signals

such as speech. In the simulations carried out, the value of was typically fixed at a

small number like 0.0005. The FXLMS algorithm was prone to instability if the step size

was increased beyond the aforementioned value. The step size of the normalized LMS

algorithm used with the subband system was also limited to the same small value to

prevent instability.

4.1 Performance of the Subband ANC system with sine waves

The system was first evaluated using sine waves at different frequencies. The

frequency of the input waves was chosen so as to represent the entire gamut of the

frequency spectrum of interest. If f 1 and f 2 are the two frequencies of interest, the input

noise signal d(n) was computed as


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)2cos()2cos()( 21 n f f

n f f

nd S S

+= 4.1

The single band FXLMS algorithm and the subband FXNLMS algorithm were then

simulated using the signal generated using equation 4.1 as the input. The MSE plots were

then calculated by ensemble averaging the residual error signals over 512 separate runs

with the input wave files shifted slightly in phase at each trial.

The performance of the single band system is known to be best at the lower

frequencies and gradually tapers off as the frequency of the noise increases. Figures 4.3

and 4.4 show the time plots and MSE plots of the single band and subband systems for

sine waves at a 30Hz frequency. We can see that the subband algorithm has a much faster

convergence than the single band system.


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Fig. 4.3. PSD and time plots for sine waves at 30Hz.

Fig. 4.4. MSE plot for sine waves at 30Hz.


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The performance of the subband system was then evaluated using sine waves at two

distinct frequencies. These frequencies were chosen so that there was one frequency

component in each of the bands used. Figure 4.5 and 4.6 show the time plots for sine

waves at 300Hz and 2000Hz. Figures 4.7 and 4.8 show the time plots and MSE plots for

sine waves at 600Hz and 2500Hz.

Fig. 4.5. PSD of input noise and time plots for sine waves at 300Hz and 2000Hz.


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Fig. 4.6. MSE plots for sine waves at 300Hz and 2000Hz.

Fig. 4.7. PSD of input noise and time plots for sine waves at 600Hz and 2500Hz.


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Fig. 4.8. MSE plot for sine waves at 600Hz and 2500Hz.

We can see that the subband system had a much faster convergence rate when compared

to the single band FXLMS algorithm. Further it was found that the performance of the

subband method did not deteriorate as the primary frequency of the noise to be cancelled

increased. Figures 4.9 and 4.10 show the time plots and the MSE plot for sine waves at

4000Hz. We can see that the convergence of the subband FXNLMS algorithm was not

adversely affected.


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Fig. 4.9. PSD of input noise and time plots for sine waves at 4000Hz.

Fig. 4.10. MSE plot of sine waves at 4000Hz.


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Fig. 4.12. 4th order bandpass IIR filter with a passband of 1250Hz-1500Hz.

Colored noise thus generated was then used as the input to the single band and subband

ANC algorithms to compare their relative performance in real world conditions. 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. Time and resource constraints prevented more extensive simulations.

However, the relative shapes of the MSE plots remained the same as we average across a

larger number of simulations while smoothening out the peaks in the curves.

The simulations using the colored noise input showed that the performance of the

subband FXNLMS algorithm was superior when compared to the single band system.

The convergence of the subband ANC system was found to be significantly faster over a


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large spectrum of frequencies. The same strategy was adopted to quantify the

performance of the subband system with colored noise as input. Figures 4.13 and 4.14

show the time plots and MSE plot for colored noise with a passband of up to 250Hz.

Fig. 4.13. PSD of input noise and time plots for colored noise at 0-100Hz.


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Fig. 4.14. MSE plot for colored noise at 0-100Hz.

We can see from the plots that the subband method showed significantly better

convergence at the lower frequencies. Ambient noise tends to have peaks at certain

dominant frequencies based on the source of the noise as illustrated in Figures 3.1 and 3.2

in Chapter 3. The subband ANC algorithm was therefore tested with colored noise at

different frequencies. The input signal was generated by adding noise at widely separated

frequencies. Figures 4.15 and 4.16 show the time plots and MSE plot for noise at 500Hz

and 1500Hz. We can see that the subband ANC algorithm had a much faster convergence

when compared to the single band algorithm.


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Fig. 4.17. PSD of primary noise and time plots for noise at 750-1000Hz and 2000-2250Hz.

Fig. 4.18. MSE plot for noise at 750-1000Hz and 2000-2250Hz.


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The subband algorithm was found to have a much faster rate of convergence when

compared to the single band system. The performance of the system was further validated

by evaluating the two systems using noise at higher frequencies. Figures 4.19 and 4.20

show the time plots and psd plots for noise at 3000Hz.

Fig. 4.19. PSD of primary noise and time plots for noise at 3000-3250Hz.


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Fig. 4.20. MSE plots for noise at 3000-3250Hz.

The performance of the subband system for noise at different frequencies is summarized

in Table 4.1.

Frequency of primarynoise signal

Noiseattenuation of

single bandalgorithm

Noiseattenuation of

subbandalgorithm

0-100Hz 14.4dB 16dB

500-750Hz and 1500-1750Hz 5.66dB 10.03dB

750-1000Hz and 2000-2250Hz 6.31dB 11.9dB

3000-3250Hz 9.7dB 15.79dB

Table 4.1. Noise attenuation of subband system for noise at different frequencies.


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The subband ANC algorithm was found to perform much better across all frequencies.

The performance of the subband system was significantly better when noise at different

frequencies was combined. Since most real world ambient noise tend to be wideband

signals with more than one dominant frequency, the subband system would be expected

to have a much bigger performance advantage for real world signals.


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CHAPTER 5

CONCLUSIONS AND FUTURE WORK

This thesis addressed the problem of attenuating loud steady state noise using the

technique of Active Noise Cancellation. A novel subband ANC system was proposed,

where the residual error signal was split into distinct frequency bands and the FXNLMS

algorithm was applied individually on each of those frequency bands. The results

established that 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. The major drawback of traditional single

band ANC algorithms is that the 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. The 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 frequencycomponents that are well separated in the frequency spectrum. The results of the

simulations using colored noise at different frequencies, showed, that by carefully


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detailed quantization analysis of the algorithm. Preliminary quantization analysis of the

single band ANC system was carried out by implementing the algorithm in floating point

C and using Texas Instruments FaQT tool. The tool showed that there were a

significantly large percentage of underflows and overflows when the algorithm was

implemented using 16 bits. Implementing the system on a portable DSP system would

then allow the study of the effects of the acoustic summing junction. Alternate methods

of estimating the secondary path by taking into account the effects of the transfer function

of the ear can also be investigated so as to minimize the noise at the ear canal itself rather

than the noise at the error microphone.


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REFERENCES

[1] P. Lueg, Process of silencing sound oscillations, U.S Patent 2,043,416 , June 9,

1936.

[2] S M Kuo and D.R.Morgan, Active Noise Control: a tutorial review, Proceedings

of the IEEE, Volume 87, Number 6, June 1999.

[3] S M Kuo and D R Morgan, Active Noise Control Systems: algorithms and DSP

implementations, John Wiley and Sons, New York, 1996.

[4] H F Olson and E G May, Electronic Sound Absorber, The Journal of the Acoustic

Society of America, Volume 25, Number 6, November 1953.

[5] B Widrow and S D Stearns, Adaptive Signal Processing, Prentice-Hall, Inc.

Englewood Cliffs, N.J, 1985.

[6] J C Burgess, Active adaptive sound control in a duct: A computer simulation, The

Journal of the Acoustic Society of America, Volume 70, Number 3, September

1981.

[7] D R Morgan, An Analysis of Multiple Correlation Cancellation Loops with a

Filter in the Auxiliary Path, IEEE Transactions of Acoustic, Speech and SignalProcessing, Volume ASSP-28, Number 4, August 1980.

[8] S J Elliott and P A Nelson, Active Noise Control, IEEE Signal Processing

Magazine, October 1993.


75/79


76/79

68

[19] D Vijayan, Feedback Active Noise Control Systems, Masters thesis, Northern

Illinois University, 1994.

[20] G B B Chaplin and R A Smith, Method of and apparatus for canceling vibrations

from a source of repetitive vibrations, U.S Patent 4,566,118, Jan 21, 1986.

[21] A V Oppenheim, E Weinstein, K C Zangi, M Feder, D Gauger, Single Sensor

Active Noise Cancellation Based on the EM Algorithm, Proc. ICASSP, Vol. I,

pp.277-280, 1992.

[22] A V Oppenheim, E Weinstein, K C Zangi, M Feder, D Gauger, Single-Sensor

Active Noise Cancellation, IEEE Transactions on Speech and Audio Processing,

Vol. 2 No. 2, April 1994.

[23] L J Eriksson, M C Allie, D E Melton, S R Popovich, T A Laak, Fully AdaptiveGeneralized Recursive Control Systems for Active Acoustic Attenuation, Proc.

ICASSP, Vol. II, 1994.

[24] G M Davis, Noise Reduction in Speech Applications, CRC Press, London, UK,

April 2002.

[25] S M Kuo, H Chuang, P Mallela, Integrated hands-free cellular, active noise

control and audio system, IEEE Transactions on Consumer Electronics, Vol. 39,

pp. 522-532, August 1993.

[26] J Chaoui, S de Gregorio, G Gallisian, Y Masse, DSP-Based Solution for Ambient

Noise Reduction in Mobile Phones, Proc. ICASSP, Vol. 4, 1999.

[27] D C Swanson, Active Noise attenuation using a self-tuning regulator as the

adaptive control algorithm, Proc. Inter-Noise, pp. 467-470, 1989.

[28] D Graupe and A J Efron, An output-whitening approach to adaptive noise

cancellation, IEEE Transactions on Circuits and Systems, Vol. 38, pp. 1306-1313,

November 1991.

[29] S J Elliott, I M Stothers, P A Nelson, A M McDonald, D C Quinn, T Saunders,

The active control of engine noise inside cars, Proc. Inter-Noise, pp. 987-990,

1988.


77/79

69

[30] S M Kuo and B M Finn, A general multi-channel filtered LMS algorithm for 3-D

active noise control systems, Proc. 2 nd International Conference Recent

Developments in Air- and Structure-Borne Sound Vibration, pp. 345-352, 1992.

[31] S J Elliott, I M Stothers, P A Nelson, A multiple error LMS Algorithm and its

applications to the active control of sound and vibrations, IEEE Transactions

Acoustics, Speech, Signal Processing, ASSP-35, 1423-1434, Oct. 1987.

[32] D E Melton and R A Greiner, Adaptive feedforward multiple-input, multiple-

output active noise control, Proceedings of ICASSP, Vol. II, pp. 229-232, 1992.

[33] S Laugesen and S J Elliott, Multichannel active control of sound in a reverberant

room, IEEE Transactions on Signal Processing, Vol. I, 241-249, April 1993.

[34] Q Shen and A Spanias, Time and Frequency Domain X-Block LMS Algorithmsfor Single Channel Active Noise Control, Proc. Second International Congress on

Recent Developments in Air- and Structure-Borne Sound and Vibration, pp. 353-

359, March 1992.

[35] Q Shen and A Spanias, Frequency Domain Adaptive Algorithms for Multi-

Channel Active Sound Control, Proc. Recent Advances in Active Control of

Sound Vibration, pp. 755-766, 1993.

[36] K M Reichard and D C Swanson, Frequency domain implementation of the

filtered-X algorithm with online system identification, Proc. Recent Advances in

Active Sound Vibration, pp. 562-573, 1993.

[37] P F Feintuch, N J Bershad and A K Lo, A frequency domain model for filtered

LMS algorithms stability analysis, design and elimination of the training mode,

IEEE Transactions on Signal Processing, Vol. 41, pp. 1518-1531, April 1993.

[38] J J Shynk, Frequency Domain and multirate adaptive filtering, IEEE Signal

Processing Magazine, Vol 9, pp. 14-37, Jan 1992.

[39] D R Morgan and J C Thi, A Delayless Subband Adaptive Filter Architecture,

IEEE Transactions on Signal Processing, Vol. 43, No. 8, August 1995.

[40] J C Thi and D R Morgan, Delayless Subband Active Noise Control, Proc.

ICASSP, Vol. 1, pp. 181-184, 1993.


78/79

70

[41] 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.

[42] A Hussain and D R Campbell, Intelligibility improvements using binaural diverse

sub-band processing applied to speech corrupted with automobile noise, IEEE

Proc. Visual Image Signal Processing, Vol. 148, No.2, April 2001.

[43] A Gilloire and M Vetterli, Adaptive Filtering in sub-bands, Proc. ICASSP, Vol. 3,

pp. 1572-1575, 1988.

[44] 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.[45] M R Petraglia and R G Alves, New Results on Adaptive Filtering Using Filter

Banks, IEEE International Symposium on Circuits and Systems, 1997.

[46] R G Alves, M R Petraglia and P S R Diniz, Convergence Analysis of an

Oversampled Subband Adaptive Filtering Structure Using Global Error, Proc.

ICASSP, Vol. 1, pp. 468-471, 2000.

[47] Texas Instruments Inc., DHP Hearing Development Kit for DHP 100 Users

Guide, SPRU551, September 2001.

[48] T E Quatieri, Discrete time speech signal processing principles and practices,

Prentice Hall, N J, October 2001.

[49] J F Kaiser, On a simple algorithm to calculate the energy of a signal, Proc.

ICASSP, Vol. 1, pp. 381-384, 1990.


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VITA

Bharath Madhusudan Siravara was born in Bangalore, India, on June 4, 1977, the son of

Shubha Madhusudan and Madhusudan Siravara. After completing his work at Sri

Aurobindo Memorial School, Bangalore, India, in 1993, he entered the

Jayachamarajendra College of Engineering at Mysore, India. During the summer of 1998

he worked as an intern in Deutsche Software, Bangalore. He received the degree of

Bachelor of Engineering with a major in Computer Science and Engineering from the

University of Mysore in August 1999. During the following year he was employed as a

Software Engineer in IBM and later in Texas Instruments, Bangalore, India. In August

2000 he entered the Graduate School of The University of Texas at Dallas.

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