The main goal of this paper is to present a simulation scheme to simulate an adaptive filter using LMS (Least mean square) adaptive algorithm for noise cancellation. The main objective of the noise cancellation is to estimate the noise signal and to subtract it from original input signal plus noise signal and hence to obtain the noise free signal. There is an alternative method called adaptive noise cancellation for estimating a speech signal corrupted by an additive noise or interference. This method uses a primary input signal that contains the speech signal and a reference input containing noise. The reference input is adaptively filtered and subtracted from the primary input signal to obtain the estimated signal. In this method the desired signal corrupted by an additive noise can be recovered by an adaptive noise canceller using LMS (least mean square) algorithm. This adaptive noise canceller is useful to improve the S/N ratio. Here we estimate the adaptive filter using Labview /MATLAB/SIMULINK environment . For achieving the goal we also use modern algorithms like ANFIS, FIS and Neural Network and compare the PSD of all the algorithms.

1. 1
PROJECT REPORT ON
“ACTIVE NOISE CANCELLATION IN A LABORATORY DUCT USING FUZZY
LOGIC AND NEURAL NETWORK ”
Submitted by-
Rishikesh 11-1-6-002
Jigmi Basumatary 11-1-6-018
Abdul Khaliq 11-1-6-029
Under the guidance of
Mr. Sudarsan Sahoo
Asst. Professor. Electronics and Instrumentation Department.
DEPARTMENT OF ELECTRONICS AND INSTRUMENTATION
NATIONAL INSTITUTE OF TECHNOLOGY
SILCHAR, ASSAM 780010
SESSION: JAN.- MAY., 2015.

2. 2
CERTIFICATE OF APPROVAL
This is to certify that the exposition titled “ACTIVE NOISE CANCELLATION IN
LABORATORYDUCT DUCT USING FUZZY LOGIC AND NEURAL NETORK” carried
out by following 8th semester students-
i) Rishikesh
ii) Jigmi Basumatary
iii) Abdul Khaliq
of Department of Electronics and instrumentation, National Institute of Technology, Slichar, is a
valid work carried out by them during the academic Jan-May 2015 under my supervision and
guidance.
(Mr. Sudarsan Sahoo)
Asst. Professor Electronics and Instrumentation Department.

3. 3
DECLARATION
We hereby declare that the work project on “Active Noise Cancellation in a LABORATORY
DUCT ” is a real work carried out by us under the guidance of Mr. Sudarsan Sahoo, during
academy session Jan.- May 2015 and this work has not been submitted for similar purpose
anywhere else except to department of Electronics and Instrumentation, National Institute of
Technology, Silchar.
Date: 5th May 2015 Rishikesh
Place: Silchar
Jigmi Basumatary
Abdul Khaliq

4. 4
CONTENTS
1 Introduction
1.1 Overview of the Project
1.2 Scope of this project
1.3 Division of Project
11
2 Literature Review
2.1 Literature Survey
13
3 Adaptive Filtering
3.1 Introduction
3.2 Adaptive Filtering System Configuration
3.3 Approach for Active Noise Control
16
4 Adaptive Algorithm
4.1 Introduction
4.2 Adaptive Algorithm
23
5 Hardware and Software Description
5.1 Hardware Description
5.2 LabVIEW
5.3 MATLab
30
6 Result and Discussion
6.1 Active Noise Cancellation System Design in LabVIEW
6.2 Low frequency noise cancellation simulation in MatLab
6.3 Active Noise Cancellation System Design in FIS
6.4 Active Noise Cancellation System Design in NN
6.5 Active Noise Cancellation System Design using ANFIS
33
7 Summary and Conclusion 43
8 References 44

5. 5
ABSTRACT
The main goal of this paper is to present a simulation scheme to simulate an adaptive filter
using LMS (Least mean square) adaptive algorithm for noise cancellation. The main objective of
the noise cancellation is to estimate the noise signal and to subtract it from original input signal
plus noise signal and hence to obtain the noise free signal. There is an alternative method called
adaptive noise cancellation for estimating a speech signal corrupted by an additive noise or
interference. This method uses a primary input signal that contains the speech signal and a
reference input containing noise. The reference input is adaptively filtered and subtracted from the
primary input signal to obtain the estimated signal. In this method the desired signal corrupted by
an additive noise can be recovered by an adaptive noise canceller using LMS (least mean square)
algorithm. This adaptive noise canceller is useful to improve the S/N ratio. Here we estimate the
adaptive filter using Labview /MATLAB/SIMULINK environment . For achieving the goal we
also use modern algorithms like ANFIS, FIS and Neural Network and compare the PSD of all the
algorithms.

6. 6
ACKNOWLEDGEMENT
Words often fail to pay one’s gratitude oneself, still we would like to convey our
sincere thanks to Mr. Sudarsan Sahoo, supervisor at every stage of completion of our project and
providing us with valuable material and guidance whenever we felt the need. Also we would like
to thank everybody who directly or indirectly helped us in successfully completion of our project.
Our special thanks to Mr. L.S.Lashkar, HOD (i/c), department of Electronics and
Instrumentation for helping us in the completion of project work and its report submission.
Rishikesh (11-1-6-002)
Jigmi Basumatary (11-1-6-018)
Abdul khaliq (11-1-6-029)

7. 7
LIST OF FIGURES
NO TITLE PAGE NO
1.1 Noise Control Classification 12
2.1 Timeline ofNoise Cancellation Techniques 13
3.1 Adaptive System Identification Configuration 16
3.2 Adaptive Noise Cancellation Configuration 17
3.3 Linear Prediction Configuration 18
3.4 Adaptive Inverse Configuration 18
3.5 Feed Forward Arrangement 19
3.6 Feedback connection 19
3.7 Block diagram ANC of duct system 20
3.8 Feedforward Experimental Setup of duct system 20
3.9 Feed Forward Path estimation arrangement 21
3.10 Feed Back Path Arrangement 21
3.11 Single Channel feed-forward ANC 22
4.1 Logic Flow Diagram 24
4.2 Filtered-X arrangement 25
4.3 Input Membership Function 26
4.4 Rule Base 26
4.5 Schematic Diagram of Noise Cancellation ANFIS 28
4.6 Structure of Fuzzy Neuro Network 29
5.1 NI PXI 30
5.2 NI cRIO 31
6.1 LabVIEW Fx-LMS Arrangement 33
6.2 Noise Residue and Control Signal 33
6.3 Noise Residue and Control Signal in Frequency Domain 34
6.4 Identification Error and Estimated Coefficient of Secondary
path
34
6.5 PSD Before FxLMS 34
6.6 PSD After FxLMS 35
6.7 Reference Signal and Noise residue from FIS 35

8. 8
6.8 PSD Before Applying Fuzzy Filter 36
6.9 PSD After Applying a Fuzzy Filter 36
6.10 Input and Noise Signal 37
6.11 Input and Estimated Signal 37
6.12 PSD Before Neural Filter 38
6.13 PSD After Neural Filter 38
6.14 Desire Signal 39
6.15 Noise Signal 39
6.16 MeasuredSignal 40
6.17 Inference Signal 40
6.18 Noise Residue in ANFIS 43
6.19 PSD Before ANFIS 43
6.20 PSD After ANFIS 42

9. 9
LIST OF TABLES
NO TITLE PAGE NO
2.1 Literature survey on Noise Cancellation techniques using
Adaptive Control
13

10. 10
List of Acronyms :
1. ANC Adaptive Noise Control
2. FIS Fuzzy Inference System
3. NN Neural Network
4. PSD PowerSpectralDensity
5. ANFIS Adaptive Neurro Fuzzy Inference System
6. LMS LeastMean Square
7. FxLMS Filtered LeastMeanSquare
8. PXI PCI Extensible for Instrumentation
9. ADC Analog to Digital Convertor
10. cRIO CompactRealtime Input Output
11. DAC Digital to Analog Converter
12. DSP Digital SignalProcessing
13. LabVIEW Laboratory Virtual Instrumentation
Engineering WorkBench

11. 11
CHAPTER-1
INTRODUCTION
1.1 Overview of project
This Project involves the principles of Adaptive Noise Control (ANC) and its
implementation in a Laboratory duct system. The principle of adaptive noise cancellation is to
obtain an estimate of the noise signal and subtract it from the corrupted signal. Adaptive noise
Cancellation is an alternative technique of estimating signals corrupted by additive noise or
interference. Acoustic noise problems become more and more evident as increased numbers of
industrial equipment such as engines, blowers, fans, transformers, and compressors are in use. The
traditional approach to acoustic noise control uses passive techniques such as enclosures, barriers,
and silencers to attenuate the undesired noise. These passive silencers are valued for their high
attenuation over a broad frequency range; however, they are relatively large, costly, and ineffective
at low frequencies. Mechanical vibration is another related type of noise that commonly creates
problems in all areas of transportation and manufacturing, as well as with many household
appliances. The ANC system efficiently attenuates low-frequency noise. ANC using signal
processing is an emerging technology that offers the unique ability to control spectral shape, to
allow flexible system operation, and to provide low lifetime cost.
The main purpose of the active sound control is to provide higher noise
reduction at low frequencies. Adaptive noise Cancellation is an alternative technique of estimating
signals corrupted by additive noise or interference. Its advantage lies in that, with no a priori
estimates of signal or noise, levels of noise rejection are attainable that would be difficult or
impossible to achieve by other signal processing methods of removing noise .ANC is developing
rapidly because it permits improvements in noise control, often with potential benefits in size,
weight, volume, and cost. Adaptive filters adjust their coefficients to minimize an error signal and
can be realized as (transversal) finite impulse response (FIR), (recursive) infinite impulse response
(IIR) and transform-domain filters. The most common form of adaptive filter is the transversal
filter using the LMS algorithm. Although ANC has been around for quite some time, the
technology is still under development and looking for widespread practical applications .There are
some modern technique of noise cancellation i.e. noise cancellation using ANFIS, Fuzzy Inference
System and Neural Network also perform under this project.

12. 12
1.2 Scope of thesis project
The scope of the thesis is to develop a Noise Control in Laboratory Duct that enable students
to perform noise control in laboratory duct experiments such as system identification, active
control of noise from a remote computer, etc. This includes measurement and analysis of noise
and configuring the hardware for estimation and noise control in laboratory duct experiments.
1.3 Division of project
The development for Noise Control in Laboratory Duct involves the study of duct system and
noise setup.
Fig 1.1 Noise Control Classification
Noise control
Active noise control
Adaptive Non-Adaptive
Passive noise control

13. 13
CHAPTER-2
LITERATURE REVIEW
In the early 1960’s first system for noise cancellation used a simple delay and invert approach but
the variability of the real world components limited their effectiveness. In the mid 1970’s a major
step forward took place with the applications of adaptive filters to generate anti-noise. This greatly
enhanced the effectiveness of the systems. A second breakthrough in the mid 1970’s was the
recognition that many noise sources particularly those made my man-made machines exhibit
periodic or tonal noise.
Practical applications of this active noise control (ANC) still has to wait as
the electrical technology availability at that time was not sufficient for implementing in the
systems. Now digital computer technology has evolved to the point where cost effective DSP
microprocessors can perform the complex calculations involved in Active noise control. Since its
beginning, considerable effort has been devoted to the theoretical and practical development of
ANC systems with the major developments coming in the past twenty years
Fig 2.1 Timeline of Noise Cancellation Techniques
Table 2.1 Literature survey on Noise Cancellation techniques using Adaptive Control
Sl.No Author/Title/Paper Objective of study Major findings

14. 14
1. Lifu Wua, Xiaojun Qiu,
YecaiGuo, “A simplified
adaptive feedback active
noise control system”
Applied Acoustics 81
(2014) 40–46
1. Purpose a simplified
adaptive feedback active noise
control system which adopts
the error signal directly as the
reference signal in an adaptive
feedforward control system
and utilizes the leaky filtered-x
LMS algorithm to update the
controller.
2. The convergence properties
of the proposal system are
investigated.
1. It is advantageous in
computational load and ease of
implementation because of the
elimination of the convolution
operation required in the
conventional IMC based
system.
2. Tabatabaeiardekani, W.H
Abdulla, “On the
convergence of real-time
active noise control
systems” Signal Processing
91 (2011) 1262–1274
To conduct a new convergence
analysis for Fx-LMS based
active noise control systems
with band-limited white noise
and moving average secondary
paths
The adaptation size leading to
the fastest convergence rate is
derived .
3. Guilhermede Souza Papini,
“Active noise control for
small diameter exhaustion
system” ABCM
Symposium Series in
Mechatronics - Vol. 3 -
pp.148-156
Considering a feedforward
ANC system for active noise
control for a small diameter
exhaust system using FXLMS
algorithm.
In this work, the first steps of an
active noise control are
developed for an exhaustion
system. The FXLMS algorithm
canhelp an ANCsystem to have
a high level of noise attenuation
regardless of the single-tone
noise source.
4. Ho.-Wuk Kim, Hong-sug
Park,Sang-kwon
Lee,”Modefied –filtered-u
LMS algo for ANC & its
application to a short
acoustic duct” Mechanical
ssytems and signal
processing25(2011)475484
To develop a new adaptive
algorithm for active noise
control (ANC) that can be
effectively applicable to a
short acoustic duct, where the
stability and fast convergence
of ANC system is particularly
important.
The new algorithm, called the
modified-filtered-u LMS
algorithm (MFU-LMS), is
developed based on the
recursive filtered-u LMS
algorithm (FU-LMS)
incorporating the simple hyper-
stable adaptive recursive filter
(SHARF) to ensure the control
stability and the variable step
size to enhance the convergence
rate.
5. Masaki Kobayashi, yasaku
tanaka,” Active noise
control using SSFC
adaptive algorithm”
Electronics and
Communications in Japan,
Vol. 97, No. 5, 2014,
1328–1333
A comparison of the required
degree of the adaptive filter to
the conventional system using
the Filtered-x adaptive
algorithm is presented
Purposed a pre-inversed ANC
system that does not use a
replica of secondary path
causing unstability. The inverse
function of the secondary path is
estimated by SSFC (Square sum
of correlation function) adaptive
algorithm which is robust to
disturbances.

15. 15
6. S.Hu, R.Rajamani,
”Directional cancellation of
acoustic noise for home
window applications”
Applied Acoustics 74
(2013) 467–477
To design a new system which
can be able to accurately
preserve desired internal sound
while cancelling uncorrelated
external noise using
feedforward algorithms.
This paper proposed to integrate
the FXLMS feedforward ANC
system with a wave separation
algorithm, which separates
externalsound from other sound
in the environment. The
resulting new ANC system used
the separated external sound
from the wave separation for
reference and error signals
instead of direct microphone
measurements.
7. ZhenyuYang. Active noise
control for a 1-D acoustic
duct usingfeedback
control techniques;
Modellingandsimulation.
WEAS Transactionson
Systems, 3(1):46-54, Jan.
2004.
Derive the state-space models
as well as the transfer function
based on physical principles.
To simulate tests using a
simple lag compensator and
show a bright potential of using
feedback control techniques in
the ANC design
The ANC design can be
formulated into a set of standard
feedback control design
problems. A simple lag
compensator is developed for
the considered system, and
simulation tests under different
situations show the bright
potential of using feedback
control in the ANC design1.

16. 16
CHAPTER-3
Adaptive Filtering
3.1 Introduction
Digital signal processing (DSP) has been a major player in the current technical advancements such
as noise filtering, system identification, and voice prediction. Standard DSP techniques, however, are
not enough to solve these problems quickly and obtain acceptable results. Adaptive filtering
techniques must be implemented to promote accurate solutions and a timely convergence to that
solution.
3.2 Adaptive Filtering System Configurations
There are four major types of adaptive filtering configurations; adaptive system identification,
adaptive noise cancellation, adaptive linear prediction, and adaptive inverse system. All of the above
systems are similar in the implementation of the algorithm, but different in system configuration. All
4 systems have the same general parts; an input x(n), a desired result d(n), an output y(n), an adaptive
transfer function w(n), and an error signal e(n) which is the difference between the desired output
u(n) and the actual output y(n). In addition to these parts, the system identification and the inverse
system configurations have an unknown linear system u(n) that can receive an input and give a linear
output to the given input.
3.2.1Adaptive System Identification Configuration
The adaptive system identification is primarily responsible for determining a discrete estimation of
the transfer function for an unknown digital or analog system. The same input x(n) is applied to both
the adaptive filter and the unknown system from which the outputs are compared (see figure 1). The
output of the adaptive filter y(n) is subtracted from the output of the unknown
system resulting in a desired signal d(n). The resulting difference is an error signal e(n) used to
manipulate the filtercoefficientsof the adaptive system trending towards an error signal of zero.

17. 17
After a number of iterations of this process are performed, and if the system is designed correctly, the
adaptive filter’s transfer function will converge to, or near to, the unknown system’s transfer
function. For this configuration, the error signal does not have to go to zero, although convergence to
zero is the ideal situation, to closely approximate the given system. There will, however, be a
difference between adaptive filter transfer function and the unknown system transfer function if the
error is nonzero and the magnitude of that difference will be directly related to the magnitude of the
error signal.
Additionally the order of the adaptive system will affect the smallest error that the system can obtain.
If there are insufficient coefficients in the adaptive system to model the unknown system, it is said to
be under specified. This condition may cause the error to converge to a nonzero constant instead of
zero. In contrast, if the adaptive filter is over specified, meaning that there is more coefficients
needed to modelled a unknown system, the error will converge to zero, but it will increase the time it
take to converge the filter.
3.2.2 Adaptive Noise Cancellation Configuration
The second configuration is the adaptive noise cancellation configuration as shown in figure 2.
In this configuration the input x(n), a noise source N1(n), is compared with a desired signal d(n),
which consists of a signal s(n) corrupted by another noise N0(n). The adaptive filter coefficients
adapt to cause the error signal to be a noiseless version of the signal s(n).

18. 18
Both of the noise signals for this configuration need to be uncorrelated to the signal s(n). In
addition, the noise sources must be correlated to each other in some way, preferably equal, to get
the best results.
Do to the nature of the error signal, the error signal will never become zero. The error signal
should converge to the signal s(n), but not converge to the exact signal. In other words, the
difference between the signal s(n) and the error signal e(n) will always be greater than zero. The
only option is to minimize the difference between those two signals.
3.2.3 Adaptive Linear Prediction Configuration
Adaptive linear prediction is the third type of adaptive configuration (see figure 3). This configuration
essentially performs two operations. The first operation, if the output is taken from the error signal
e(n), is linear prediction. The adaptive filter coefficients are being trained to predict, from the statistics
of the input signal x(n), what the next input signal will be. The second operation, if the output is taken
from y(n), is a noise filter similar to the adaptive noise cancellation outlined in the previous section.
As in the previous section, neither the linear prediction output nor the noise cancellation output will
converge to an error of zero. This is true for the linear prediction output because if the error signal did
converge to zero, this would mean that the input signal x(n) is entirely deterministic, in which case we
would not need to transmit any information at all.
In the case of the noise filtering output, as outlined in the previous section, y(n) will converge to
the noiseless version of the input signal.
3.2.4 Adaptive Inverse System Configuration
The final filter configuration is the adaptive inverse system configuration as shown in figure 4. The
goal of the adaptive filter here is to model the inverse of the unknown system u(n). This is
particularly useful in adaptive equalization where the goal of the filter is to eliminate any spectral
changes that are caused by a prior system or transmission line. The way this filter works is as
follows. The input x(n) is sent through the unknown filter u(n) and then through the adaptive filter
resulting in an output y(n). The input is also sent through a delay to attain d(n). As the error signal is

19. 19
converging to zero, the adaptive filter coefficients w(n) are converging to the inverse of the unknown
system u(n).
For this configuration, as for the system identification configuration, the error can theoretically
go to zero. This will only be true, however, if the unknown system consists only of a finite
number of poles or the adaptive filter is an IIR filter. If neither of these conditions are true, the
system will converge only to a constant due to the limited number of zeroes available in an FIR
system.
3.3 Approaches of ANC
The following are the connection schemes of noise controlling using adaptive filter
Fig 3.5 Feed Forward Arrangement
3.3.1 Feed forward
As shown in the figure adove it uses reference noise and error are applied to the
controller. This system is mostly used over feedback because of inherent stability
3.3.2 Feed back

20. 20
In this system only one output and single input Error is fed to the controlle
Fig.3.6 Feedback connection
Fig 3.7 Block diagram ANC of duct system
Fig 3.8 Feedforward Experimental Setup of duct system

21. 21
3.3.3 Forward path estimation
The control signal path from the DAC, low pass filter, amplifier, anti-noise speaker,
acoustic path, error microphone, low pass filter, amplifier and ADC form the forward path of the
ANC system. To estimate the forward path an identification signal, i.e. band limited random noise
may be used to excite the physical forward path. The signal x(n) shown in the Figure 6.2 is the
identification signal and signal d(n) sensed by the error microphone is the desired signa fed to the
DSP. System identification based on the LMS algorithm may be utilized in the DSP.
Here the error signal e(n) is difference between the adaptive filter’s output signal y(n) and the
desired signal d(n).
Fig 3.9 Feed Forward Path estimation arrangement

22. 22
3.3.4 Feedback path estimation
Fig 3.10 Feed Back Path Arrangement
In the single channel feed forward ANC system a reference microphone which is used to
sense the reference signal ideally will also sense anti-noise generated by anti-noise speaker, known
as acoustic feedback. This feedback path from DAC, low pass filter, amplifier, anti-noise speaker,
acoustic path, reference microphone, low pass filter, amplifier, ADC may be estimated similar to
forward path estimation. In this system identification problem signal from reference microphone
is used as desired signal d(n) as shown in Figure
.
3.3.5 Single channel feed-forward ANC
In the current laboratory setup the user can perform ANC experiments with or without
reference microphone. In this section steps involved in performing single channel feed forward
ANC experiments using the remote laboratory are discussed. A block diagram of single channel
feedforward ANC system is shown in Figure

23. 23
Fig 3.11 Single Channel feed-forward ANC
In Figure F| is the forward path estimate while B| is the feedback path estimate as
discussed in Section 6.3.1 and Section 6.3.2 respectively. The signal filtered by F| and B| are
XF|(n) and XB|(n) respectively. Reference signal sensed by the reference microphone, error
signal sensed by error microphone and the control signal fed to the control speaker are x(n),
e(n) and y(n) in the Figure 6.8. In this section reference microphone 2 is used as a reference
microphone. If the user carry out ANC experiments without using any reference microphone
then feedback path will not be estimated.

24. 24
CHAPTER-4
ADAPTIVE FILTER ALGORITHM
4.1 Introduction
Adaptive noise Cancellation is an alternative technique of estimating signals corrupted by
additive noise or interference. Its advantage lies in that, with no appropriate estimates of signal or
noise, levels of noise rejection are attainable that would be difficult or impossible to achieve by
other signal processing methods of removing noise. Its cost, inevitably, is that it needs two inputs
a primary input containing the corrupted signal and a reference input containing noise correlated
in some unknown way with the primary noise. The reference input is adaptively filtered and
subtracted from the primary input to obtain the signal estimate. Adaptive filtering before
subtraction allows the treatment of inputs that are deterministic or stochastic, stationary or time-
variable. The effect of uncorrelated noises in primary and reference inputs, and presence of signal
components in the reference input on the ANC performance is investigated. It is shown that in the
absence of uncorrelated noises and when the reference is free of signal; noise in the primary input
can be essentially eliminated without signal distortion. A configuration of the adaptive noise
canceller that does not require a reference input and is very useful many applications is also
presented. The usual method of estimating a signal corrupted by additive noise is to pass it through
a filter that tends to suppress the noise while leaving the signal relatively unchanged i.e. direct
filtering. The design of such filters is the domain of optimal filtering, which originated with the
pioneering work of Wiener and was extended and enhanced by Kalman, Bucy and others. Filters
used for direct filtering can be either Fixed or Adaptive.
4.2 Adaptive Algorithms
4.2.1 Least MeanSquare Algorithms (LMS)
To make exact measurements of the gradient vector ▼J(n) at each iteration n, and if the step-size
parameter µ is suitably chosen then the tap-weight vector computed by using the steepest descent
algorithm would converge to the optimum wiener solution. The exact measurements of the
gradient vector are not possible and since that would require prior knowledge of both the
autocorrelation matrix R of the tap inputs and the cross correlation vector p between the tap
inputs and the desired response, the optimum wiener solution could not be reached.
Consequently, the gradient vector must be estimated from the available data when we operate in
an unknown environment. After estimating the gradient vector we get a relation by which we can
update the tap weight vector recursively as:
w(n+1)=w(n)+ µu(n)[d*(n)-uH(n)w(n)]
Where,
µ= step size parameter
uH(n)= Hermit of a matrix u

25. 25
d*(n)= Complex conjugate of d(n)
Fig 4.1 Logic Flow Diagram
We may write the result in the form of three basic relations as follows:
Filter output: (y)=wH(n)u(n)
Estimation error or error signal: e(n)=d(n)-y(n)
Tap weight adaptation: w(n+1)=w(n)+ µu(n)e*(n)
Equations (2) and (3) define the estimation error e(n), the computation of which is based on the
current estimate of the tap weight vector(n) . Note that the second term u(n)e*(n), on the right hand
side of equation (4) represents the adjustments that are applied to the current estimate of the tap
weight vector (w) . The iterative procedure is started with an initial guess w(0) .The algorithm
described by equations (2) and (3) is the complex form of the adaptive least mean square (LMS)
algorithm. At each iteration or time update, this algorithm requires knowledge of the most recent
values u(n), d(n) and w(n) The LMS algorithm is a member of the family of stochastic gradient
algorithms. In particular, when the LMS algorithm operates on stochastic inputs, the allowed set
of directions along which we “step” from one iteration to the next is quite random and therefore
cannot be thought of as consisting of true gradient directions.
4.2.2 Fuzzy Adaptive Filtered X-Algorithm

26. 26
The usual ANC system, which utilises the filtered-X algorithm, is shown in Fig. 1. In the plant
model, Hp(z) represents the primary speaker and P(z) denotes the mathematical transfer function
of the acoustic duct, the input signal xk represents the kth undesired noise sample,
and the residual noise ek is measured by an error microphone. The output signal of the filtered-X
algorithm uk drives an anti-noise speaker with transfer function Hs(z), in an attempt to cancel the
undesired noise in the duct. The acoustic transfer function from the location of the anti-noise
speaker to the error microphone Mp(z) is referred to as the error path and is represented by He(z).
The (N+1)th order adaptive active noise controller with weighting parameters.
Fig 4.2 Filtered-X arrangement
4.2.2.1 Fuzzy Sets and Membership Function
Generally speaking, the output of a (N+1)th order FIR filter is composed of the moving averages
of the past (N+1) input noise samples. Hence, one uses the past (N+1) noise samples to design
the fuzzy filter. For a (N+1)th order fuzzy ANC system, one can define M fuzzy sets F for each
input noise sample xk_i with Gaussian membership functions
where l=1,2, M, i=0,1,2,.., N and k and denotes the time samples. In (7),_xx l i are the centres
and sl xi are standard deviations of the Gaussian functions, respectively. In this study, we set
M¼7, N¼20 and the initial standard deviations equal to 0.2. Hence, each input sample xk_i, has
seven linguistic terms which initially are equally distributed in the input signal range [-1 1]; NB
(negative big), NM(negative medium), NS (negative small), AZ (almost zero),PS (positive

27. 27
small), PM (positive medium) and PB (positive big). Figure 4 shows the results of this step in
constructing a twenty-first order fuzzy FIR filter.
Fig4.3 Input Membership Function
Fig 4.4 Rule Base
In a fuzzy inference engine, fuzzy logic principles combine fuzzy rules into a mapping from an
input fuzzy set to an output fuzzy set.
4.2.2.2 Linguistic Variables and Rule Bases

28. 28
Linguistic variables are values defined by fuzzy sets. A linguistic variable such as ‘Negative
More ’ for example could consist of numbers that are equal to or between -1 and -0.1. The
conditional statements that make up the rules that govern fuzzy logic behaviour use these
linguistic variables and have an if-then syntax. These if-then rules are what make up fuzzy rule
bases. A sample if-then rule where A and B represent linguistic variables could be:
if x is A then y is B
The statement is understood to have both a premise, if ‘x is A’, and a conclusion, then ‘y is
B’. The premise also known as the antecedent returns a single number between 0 and 1
whereas the conclusion also known as the consequent assigns the fuzzy set B to the output
variable y. Another way of writing this rule using the symbols of assignment ‘=’ and
equivalence ‘==’ is:
if x == A then y = B
An if-then rule can contain multiple premises or antecedents.
For example, if velocity is high and road is wet and brakes are poor then
Similarly, the consequent of a rule may contain multiple parts.
if temperature is very hot then fan is on and throughput is reduced
4.2.2.3 Defuzzifier
The proposed filter, using a minimum the inference engine and centroid defuzzifier, is
obtained by combining the M rules defined in the previous step. The filter is represented as
To minimise the power of residual noise, the fuzzy filtered-X LMS algorithm uses the
following:

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Type equation here.
where λ is a small positive constant.
4.2.3 ANFIS
ANFIS uses a hybrid learning algorithm to identify the membership function parameters of single-
output, fuzzy inference systems (FIS). Fuzzy systems lack the ability of learning. Relying on IF-
THEN rules and logical inference, it explains its reasoning. Combination of fuzzy with neural
network controller can assist a fuzzy controller and the controller could save the time to achieve
the optimal solution.
The basic idea of combining fuzzy systems and neural networks is to design an architecture that
uses a expert knowledge of fuzzy system in addition to possessing the learning ability of a neural
network.
ANFIS cancels out the interference signal and gives better performance even if the complexity of
the signal is very high.

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The basic idea of an adaptive noise cancellation purposed here is to pass the inference signal
generated by anfis.
To estimate the interference signal d(k), we need to pick up a clean version of the noise signal n(k)
that is independent of the required signal.
ANFIS is used to estimate the unknown interference 𝑑 ̂( 𝑘). When 𝑑 ̂( 𝑘) and d(k) are close to each
other, these two get cancelled and we get the estimated output signal 𝑥 ̂( 𝑘)which is close to the
required signal.
The passage f represents the passage dynamics that the noise signal n(k) goes through.
The adaptive neuro-fuzzy inference system (anfis) is the main architecture of the controller
in adaptive noise control(ANC).
In this study the Mamdani-type of IF-THEN rule is used to construct human knowledge.
The jth fuzzy rule has the following form
Rule: IF 𝑥1 is 𝐴1𝑗 and 𝑥2is 𝐴2𝑗 and…𝑥 𝑖is 𝐴𝑖𝑗
THEN 𝑦1is 𝐶1 and 𝑦2 is 𝐶2 and … 𝑦𝑗 is 𝐶𝑗
Where 𝑥 𝑖 and 𝑦𝑗 are the input and output variables of the system, 𝐴𝑖𝑗 are the membership
functions of the antecedent part, and 𝐶𝑗
′
𝑠 are the real no. which simply cut the consequent mf at
the level of antecedent truth.
In figure 2, Layer 1 is the input layer. Each node in this layer transmits external crisp signals 𝑥_𝑖
directly to the next layer.
Layer 2 is the fuzzification layer, which maps input 𝑥_𝑖 into the fuzzy set 𝐴_𝑖𝑗.
Layer 3 is a fuzzy reasoning layer, which performs IF-condition reasoning by a min or product
operation and generates the firing strength 𝑦_𝑗^((3))
Layer4 and layer 5 performs the approximation centre of gravity (COG) defuzzification method to
generate a crisp output regarded as the final output of the control system.
The basic steps used in the computation of ANFIS in matlab are given below:

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Generate an initial conditions Sugeno-type FIS system using the matlab command genfis1 for anfis
training.
i) Give the parameters like number of MF, step size.
ii) genfis1 is used to fuzzify the training data matrix.
Start learning process using the command anfis and stop when goal is achieved or the epoch is
completed.
Anfis uses a back-propagation algorithm to identify the membership function parameters of single-
output, Sugeno type fuzzy inference systems to emulate a training data.
The final step is to evaluate the fuzzy inference system using the command “evalfis” to perform
fuzzy inference calculations.This function use to get the estimated interference signal by using the
training data and the fuzzification of the output.
CHAPTER-5
HARDWARE AND SOFTWARE DESCRIPTION
5.1 Hardware description
Hardware used in traditional laboratories for ANC experiments have to meet the specific
re-quirements of ANC system. However when duct laboratory for ANC system is designed
hardware should be capable of handling requirements from both ends i.e. from ANC system and
duct system.Following sections describe the requirement and implementation of each hardware
module used in the duct laboratory.
5.1.1 PXI

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PXI is a rugged PC-based platform for measurement and automation systems. PXI
combines PCI electrical-bus features with the modular, Eurocard packaging of CompactPCI and
then adds specialized synchronization buses and key software features. PXI is both a high-
performance and low-cost deployment platform for applications such as manufacturing test,
military and aerospace, machine monitoring, automotive, and industrial test. Developed in 1997
and launched in 1998, PXI is an open industry standard governed by the PXI Systems Alliance
(PXISA), a group of more than 70 companies chartered to promote the PXI standard, ensure
interoperability, and maintains the PXI specification.
Fig 5.1 NI PXI
Since inventing the standard in 1997 and founding the PXI Systems Alliance industry consortium
in 1998, National Instruments has been at the forefront of delivering the benefits of PXI to
engineers and scientists worldwide. With the largest selection of chassis, controllers, and timing
and synchronization and more than 600 modules, you can address virtually any engineering
challenge.
5.1.2 CRIO
CompactRIO is a reconfigurable embedded control and acquisition system. The CompactRIO
system’s rugged hardware architecture includes I/O modules, a reconfigurable FPGA chassis, and
an embedded controller. Additionally, CompactRIO is programmed with NI LabVIEW graphical
programming tools and can be used in a variety of embedded control and monitoring applications.

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Fig 5.2 NI cRIO
With the introduction of CompactRIO in 2004, National Instruments redefined the embedded
market by offering a reconfigurable solution that combines the flexibility of custom design with
the short time to market of an off-the-shelf product. CompactRIO paired with the NI LabVIEW
graphical development environment gives you the ability to create embedded control and
monitoring systems with unparalleled productivity.
5.1.3 Duct, Microphone and Speaker
The ventilation duct used in the experiment should be of length such that the lower order
acoustic modes are observable. The broadband noise used to excite the duct may be in the range
[50Hz-400Hz] so that the upper limit is well within the planar wave region of the duct. Limiting
the sound waves within the planar wave region of the duct enables the microphones to be installed
at various position of the duct for measurements. Thus a circular duct of 4m in length and 315mm
inner diameter is chosen which meets above mentioned requirements. The microphones and
speakers used in the ANC system should have at frequency response in the control band width
[50Hz-400Hz].
The microphones selected are battery powered Integrated Electronics Piezo Electric (IEPE)
microphones. These microphones have at frequency response from 20Hz to 16000Hz. In the
ventilation duct _ve microphones, reference microphones and error microphone, are installed at
di_erent positions and two Fostex 6301B3 loudspeakers (primary noise source and anti-noise
source) are installed, one at respective duct end.
5.2 LabVIEW
LabVIEW from National Instruments is a visual programming language which supports
interaction with di_erent software and hardware. Programming in LabVIEW is done by Virtual
Instruments (VI's). VIs are composed of front panel and block diagrams. Front panel shows

34. 34
the graphical view of the VI which will be visible to the end user while actual programming is
done in block diagram. LabVIEW provides facility to interact with the Code Composer Studio
automation tool using the DSP Test Integration toolkit. This toolkit provides di_erent VIs to
interact with the Code Composer Studio such as opening Code Composer Studio, compiling the
project, memory read write operations etc. Further functions can be added using LabVIEW
programming.Above discussion concerns the development environment but in order to make this
development environment remotely accessible LabVIEW provides di_erent options which are
discussed below.
5.3 Matlab
MATLAB® is a high-level language and interactive environment for numerical computation,
visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and
create models and applications. The language, tools, and built-in math functions enable you to
explore multiple approaches and reach a solution faster than with spreadsheets or traditional
programming languages, such as C/C++ or Java™.
You can use MATLAB for a range of applications, including signal processing and
communications, image and video processing, control systems, test and measurement,
computational finance, and computational biology. More than a million engineers and scientists in
industry and academia use MATLAB, the language of technical computing.
CHAPTER-6
RESULT AND DISCUSSION
6.1 Active Noise Cancellation System Designin LabVIEW
Successfully implemented the design of Active Noise Cancellation in LabVIEW

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Fig 6.1 LabVIEW Fx-LMS Arrangement
6.2 Low frequency noise cancellation simulation in MatLab
After going through a series of process and experiments to get appropriate value for step size and
filter length we get our desired result at Step size(mu)=0.9. Here in this process I have collected a
noise from my Laptop cooling fan and the recorded noise was minimized by applying FxLMS
algorithm in Matlab..
Fig 6.2 Noise Residue and Control Signal
In frequency Domain:

36. 36
Fig 6.3 Noise Residue and Control Signal in Frequency Domain
Identification Error and Estimated Coefficient of Secondary path:
Fig 6.4 Identification Error and Estimated Coefficient of Secondary path
Power spectrum of noise:
Initially the level of noise i.e before ANC was -10dB but was
attenuated to -20dB after ANC using FX-LMS Algorithm. A total noise reduction of 10 dB.
Fig 6.5 PSD Before FxLMS

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Fig 6.6 PSD After FxLMS
6.3 Active Noise Cancellation System Designin Fuzzy Logic using Mamdani
Input Reference Signal to Fuzzy System
Fig 6.7 Reference Signal and Noise residue from FIS

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Compare the Power Spectrum of Before and After applying Fuzzy Filter
Fig 6.8 PSD Before Applying Fuzzy Filter
Fig 6.9 PSD After Applying a Fuzzy Filter

39. 39
6.4 Active Noise Cancellation System Designin Neural Network
Using single Layer Neural Network with learning constant 0.05
u(t)=blue d(t)=Green
Fig 6.10 Input and Noise Signal
u(t)=blue uh(t)=Green
Fig 6.11 Input and Estimated Signal

40. 40
Fig 6.12 PSD Before Neural Filter
Fig 6.13 PSD After Neural Filter

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6.5 Active Noise Cancellation System Designusing ANFIS
Fig 6.14 Desire Signal

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Fig 6.15 Noise Signal
Fig 6.16 Measured Signal
Fig 6.17 Inference Signal

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Fig 6.18 Noise Residue in ANFIS
Fig 6.19 PSD Before ANFIS

44. 44
Fig 6.20 PSD After ANFIS

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CHAPTER-6
SUMMARY AND CONCLUSION
A Laborartory Duct ANC in which we are performed all the necessary steps required for ANC
experiment and at the end we designed and successfully perform simulation.We are successfully
implemented ANC in both artificial as well as real world noise using modern FxLMS algorithm.
We simulate our code several time by changing some of the filter parameters like step size , filter
length etc to get best result .We need to keep it in mind that it works for noise frequency ranging
from 100 to 800 Hz.
We also implement the ANC using fuzzy and neural based algorithms. And getting better result
than FxLMS.ANFIS(Adaptive Neuro Fuzzy Inference System) gives best result for Adaptive
Noise Cancellation

46. 46
CHAPTER-7
REFERENCES
1. Guilhermede Souza Papini, “Active noise control for small diameter exhaustion system”
ABCM Symposium Series in Mechatronics - Vol. 3 - pp.148-156
2. S.Hu, R.Rajamani, ”Directional cancellation of acoustic noise for home window
applications” Applied Acoustics 74 (2013) 467–477
3. Lifu Wua, Xiaojun Qiu, Yecai Guo, “A simplified adaptive feedback active noise control
system” Applied Acoustics 81 (2014) 40–46
4. Ho.-Wuk Kim, Hong-sug Park, Sang-kwon Lee,”Modefied –filtered-u LMS algo for ANC & its
application to a short acoustic duct” Mechanical sytems and signal processing 25 (2011)
475-484
5. Zhenyu Yang. Active noise control for a 1-D acoustic duct using feedback control
techniques; Modelling and simulation. WEAS Transactions on Systems, 3(1):46-54, Jan.
2004.
6. H.R pota and A.G Kelkar “modeling and control of acoustic ducts” journal of Vibration and
acoustics, Transactions of the ASME , Vol. 123, Jan 2001.
7. Zhenyu Yang and Steffen Podlech ,theoretical modeling issue in ANC for a one-dimensional
acoustic duct system Proceedings of the 2008 IEEE International Conference on Robotics
and Biomimetics Bangkok, Thailand, February 21 - 26, 2009
8. Fuller, C. R., and von Flotow, A. H., 1995, ‘‘Active control of sound and vibration,’’ IEEE
Control Syst. Mag., 16, No. 6, pp. 9–19, December.
9. Wikipedia.org (http://en.wikipedia.org/wiki/Active_noise_control).