Post on 05-Apr-2018
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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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SUBBAND FEEDBACK ACTIVE NOISE CANCELLATION
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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v
SUBBAND FEEDBACK ACTIVE NOISE CANCELLATION
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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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
Cancelingloudspeaker
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
Cancelingloudspeaker
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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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.