synopnis format

8/7/2019 Synopnis Format

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CHAMELI DEVI INSTITUTE OF TECHNOLOGY

& MANAGEMENT, INDORE

SYNOPSYS

ON

ACOUSTIC NOISE CANCELLATION

Submitted to: Submitted by:Mr. Shafi Patel Punita Sharma

0832EC071041

Ruchi Dubey

0832EC071048

Surabhi Sharma

0832EC071055

Surbhi Jain

0832EC071056


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CONTENTS

Abstract

Background Theory

Introduction (Adaptive Filter)

Block diagram

Alogrithm:-

o Lmso Nlms

Tool used (matlab)

Reference


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ABSTRACTAcoustic echo cancellation is a

common occurrence in todays

elecommunication systems. It occurs

when an audio source and sink

operate in full duplex mode, an

example of this is a hands-free

loudspeaker telephone. In this

situation the received signal is output

through the telephone loudspeaker

(audio source), this audio signal is

then reverberated through the

physical environment and picked up by the systems microphone (audio sink). The

effect is the return to the distant user of time delayed and attenuated images of their

original speech signal. The signal interference caused by acoustic echo is

distracting to both users and causes a reduction in the quality of thecommunication. This thesis focuses on the use of adaptive filtering techniques to

reduce this unwanted echo, thus increasing communication quality. Adaptive filters

are a class of filters that iteratively alter their parameters in order to minimise a

function of the difference between a

desired target output and their output.

In the case of acoustic echo in

telecommunications, the optimal

output is an echoed signal that

accurately emulates the unwanted

echo signal. This is then used to

negate the echo in the return signal.

The better the adaptive filter emulates

this echo, the more successful the

cancellation will be. This thesis

examines various techniques and

algorithms of adaptive filtering,

employing discrete signal processing

in matlab. Also a real-time

implementation of an adaptive echo cancellation system has been developed . Thetopic for this thesis is .acoustic echo cancellation using digital signal processing.

Acoustic echo occurs when an audio signal is reverberated in a real environment,

resulting in the original intended signal plus attenuated, time delayed images of

this signal. This report will focus on the occurrence of acoustic echo in

telecommunication systems. Such a system consists of coupled acoustic input and

output devices, both of which are active concurrently. An example of this is a


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hands-free telephony system. In this scenario the system has both an active

loudspeaker and microphone input operating simultaneously. The system then acts

as both a receiver and transmitter in full duplex mode. When a signal is received

by the system, it is output through the loudspeaker into an acoustic environment.

This signal is reverberated within the environment and returned to the system via

the microphone input. These reverberated signals contain time delayed images of

the original signal, which are then returned to the original senderthe occurrence of

acoustic echo in speech transmission causes signal interference and reduced quality

of communication. (figure 1.1, ak is the attenuation, tk is time delay). The method

used to cancel the echo signal is known as adaptive filtering. Adaptive filters are

dynamic filters which iteratively alter their characteristics in order to achieve an

optimal desired output. An adaptive filter algorithmically alters its parameters in

order to minimise a function of the difference between the desired output d(n) and

its actual output y(n). This function is known as the cost function of the adaptive

algorithm. Figure 1.2 shows a block diagram of the adaptive echo cancellation

system implemented throughout this thesis. Here the filter h(n) represents theimpulse response of the acoustic environment, w(n) represents the adaptive filter

used to cancel the echo signal. The adaptive filter aims to equate its output y(n) to

the desired output d(n) (the signal reverberated within the acoustic environment).

At each iteration the error signal, e(n)=d(n)-y(n), is fed back into the filter, where

the filter characteristics are altered accordingly.

This report deals with acoustic echo as applies to telecommunication systems,

although the techniques will be applicable to a variety of other disciplines.

This goals of this project are as follows:

to examine adaptive filtering techniques as they apply to acoustic echo

Cancellation.

to simulate these adaptive filtering algorithms using matlab.

to develop a real time acoustic echo cancellation system .


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BACKGROUND THEORY

In order to understand the content presented in this thesis it is first necessary to

provide some background information regarding digital signal theory. It will start

out rather elementary and then progress to more complicated matters. Later

chapters will build upon this theoretical basis in the derivation and implementationof the adaptive filtering techniques used in acoustic echo cancellation.

Acoustics

Acoustics is the interdisciplinary science that deals with the study of all

mechanical waves in gases, liquids, and solids including vibration, sound,

ultrasound and infrasound. A scientist who works in the field of acoustics is

an acoustician while someone working in the field of acoustics technology may be

called an acoustical or audio engineer. The application of acoustics can be seen inalmost all aspects of modern society with the most obvious being the audio and

noise control industries.

hearing is one of the most crucial means of survival in the animal world, and

speech is one of the most distinctive characteristics of human development and

culture. So it is no surprise that the science of acoustics spreads across so many

facets of our societymusic, medicine, architecture, industrial production, warfare

and more. Art, craft, science and technology have provoked one another to advance

the whole, as in many other fields of knowledge. Linsday's wheel of acoustics is awell accepted overview of the different fields in acoustics.

The word "acoustic" is derived from the greek word (akoustikos),

meaning "of or for hearing, ready to hear" and that from (akoustos),

"heard, audible", which in turn derives from the verb (akouo), "i hear".

The latin synonym is "sonic", after which the term sonics used to be a synonym fo

acousticsand later a branch of acoustics. After acousticians had extended their

studies to frequencies above and below the audible range, it became conventional

to identify these frequency ranges as "ultrasonic" and "infrasonic" respectively,while letting the word "acoustic" refer to the entire frequency range without limit.


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ADAPTIVE FILTERS

Introduction

Figure 3.1. Adaptive filter block diagram (farhang-boroujeny 1999, p. 120) here w

represents the coefficients of the fir filter tap weight vector, x(n) is the input vectorsamples, z-1 is a delay of one sample perios, y(n) is the adaptive filter output, d(n)

is the desired echoed signal and e(n) is the estimation error at time n. The aim of an

adaptive filter is to calculate the difference between the desired signal and the

adaptive filter output, e(n). This error signal is fed back into the adaptive filter and

its coefficients are changed algorithmically in order to minimise a function of this

difference, known as the cost function. In the case of acoustic echo cancellation,

the optimal output of the adaptive filter is equal in value to the unwanted echoed

signal. When the adaptive filter output

is equal to desired signal the error signalgoes to zero. In this situation the echoed

signal would be completely cancelled

and the far user would not hear any of

their original speech returned to them.

This section examines adaptive filters

and various algorithms utilised. The

various methods used in this thesis can

be divided into two groups based on

their cost functions. The first class are

known as mean square error (mse)

adaptive filters, they aim to minimise a

cost function equal to the expectation of

the square of the difference between the desired signal d(n), and the actual output

of the adaptive filter y(n) (equation 3.1).

(n) = e[e2 (n)] = e[(d(n) y(n))2 ]

The second class are known as recursive least squares (rls) adaptive filters and they

Aim to minimise a cost function equal to the weighted sum of the squares of the

Difference between the desired and the actual output of the adaptive filter for

different time instances. The cost function is recursive in the sense that unlike the

mse cost function, weighted previous values of the estimation error are also

considered. The cost function is shown below in equation 3.2, the parameter is in

the range of 0


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previous values to have an increasingly negligible effect on updating of the filter

tap weights (diniz 1997, p. 184). The value of 1/(1- ) is a measure of the memory

of the algorithm (farhang-boroujeny 1999, p. 420), this thesis will primarily deal

with infinite memory ,i.e. =1. The cost function for rls algorithm, (n), is stated

in equation.

Where k=1, 2, 3.n., k=1 corresponds to the time at which the rls algorithm

commences. Later we will see that in practice not all previous values are

considered, rather only the previous n (corresponding to the filter order) error

signals are considered. As stated previously, considering that the number of

processes in our ensemble averages is equal to one, the expectation of an input or

output value is equal to that actual value at a unique time instance. However, for

the purposes of deriving these algorithms, the expectation notation shall still beused.

Block Diagram of generic echo cancellation


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Least mean square (lms) algorithm

The least mean square (lms) algorithm was first developed by widrow and hoff in

1959 through their studies of pattern recognition (haykin 1991, p. 67). From there

it has become one of the most widely used algorithms in adaptive filtering. The lms

algorithm is a type of adaptive filter known as stochastic gradient-based algorithms

as it utilises the gradient vector of the filter tap weights to converge on the optimal

wiener solution. It is well known and widely used due to its computational

simplicity. It is this simplicity that has made it the benchmark against which all

other adaptive filtering algorithms are judged (haykin 1991, p. 299). With each

iteration of the lms algorithm, the filter tap weights of the adaptive filter are

updated according to the following formula (farhang-boroujeny 1999, p. 141).

w(n +1) = w(n) + 2e(n)x(n) (eq 3.7)

Here x(n) is the input vector of time delayed input values,

x(n) = [x(n) x(n-1) x(n-2) .. X(n-n+1)]t.

The vector

W(n) = [w0(n) w1(n) w2(n) .. Wn-1(n)] t

represents the coefficients of the adaptive fir filter tap weight vector at time n. The

parameter is known as the step size parameter and is a small positive constant.

This step size parameter controls the influence of the updating factor. Selection of

a suitable value for is imperative to the performance of the lms algorithm, if thevalue is too small the time the adaptive filter takes to converge on the optimal

solution will be too long; if is too large the adaptive filter becomes unstable and

its output diverges.

Derivation of the lms algorithm.

The derivation of the lms algorithm builds upon the theory of the wiener solution

for the optimal filter tap weights, wo, as outlined in section 3.2. It also depends on

the steepestdescent algorithm as stated in equation 3.8, this is a formula which

updates the filter coefficients using the current tap weight vector and the current

gradient of the cost function with respect to the filter tap weight coefficient vector,


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As the negative gradient vector points in the direction of steepest descent for the

ndimensional quadratic cost function, each recursion shifts the value of the filter

Coefficients closer toward their optimum value, which corresponds to the

minimum achievable value of the cost function, (n). This derivation is based on

diniz 1997, pp. 71-3 and farhang-boroujeny 1999, pp.139.41. The lms algorithm is

a random process implementation of the steepest descent algorithm, from equation

3.8. Here the expectation for the error signal is not known so the instantaneous

value is used as an estimate. The steepest descent algorithm then becomes equation

3.9.

The gradient of the cost function, (n), can alternatively be expressed in the

following form.

Substituting this into the steepest descent algorithm of equation 3.8, we arrive at

the recursion for the lms adaptive algorithm.

Implementation of the lms algorithm.

Each iteration of the lms algorithm requires 3 distinct steps in this order:

1. The output of the fir filter, y(n) is calculated using equation 3.12.


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2. The value of the error estimation is calculated using equation 3.13.

3. The tap weights of the fir vector are updated in preparation for the nextiteration, by equation 3.14.

The main reason for the lms algorithms popularity in adaptive filtering is its

Computational simplicity, making it easier to implement than all other commonly

used adaptive algorithms. For each iteration the lms algorithm requires 2n

additions and 2n+1 multiplications (n for calculating the output, y(n), one for

2e(n) and an additional n for the scalar by vector multiplication) (farhang-

boroujeny 1999, p. 141).


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normalised least mean square (nlms) algorithmOne of the primary disadvantages of the lms algorithm is having a fixed step size

Parameter for every iteration. This requires an understanding of the statistics of the

input signal prior to commencing the adaptive filtering operation. In practice this is

rarely achievable. Even if we assume the only signal to be input to the adaptive

echo cancellation system is speech, there are still many factors such as signal input

power and amplitude which will affect its performance.

The normalised least mean square algorithm (nlms) is an extension of the lms

Algorithm which bypasses this issue by selecting a different step size value, (n),

for each iteration of the algorithm. This step size is proportional to the inverse of

the total expected energy of the instantaneous values of the coefficients of the input

vector x(n) (farhang-boroujeny 1999, p.172). This sum of the expected energies of

the input samples is also equivalent to the dot product of the input vector with

itself, and the trace of input vectors auto-correlation matrix, r (farhang-boroujeny

1999, p.173).

The recursion formula for the nlms algorithm is stated in equation 3.16.

Derivation of the nlms algorithm.

This derivation of the normalised least mean square algorithm is based on farhang-

Boroujeny 1999, pp.172-175, and diniz 1997, pp 150-3. To derive the nlms

algorithm we consider the standard lms recursion, for which we select a variable

step size parameter, (n). This parameter is selected so that the error value , e+(n),

will be minimised using the updated filter tap weights, w(n+1), and the currentinput vector, x(n).


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Next we minimise (e+(n))2, with respect to (n). Using this we can then find a

value for (n) which forces e+(n) to zero.

This (n) is then substituted into the standard lms recursion replacing , resultingin the following.

Often the nlms algorithm is expressed as equation 3.20, this is a slight modification

of the standard nlms algorithm detailed above. Here the value of is a small

positive constant in order to avoid division by zero when the values of the input

vector are zero.

This was not implemented in the real time implementation as in practice the input

signal is never allowed to reach zero due to noise from the microphone and from

the ad codec on the texas instruments dsk. The parameter is a constant step size

value used to alter the convergence rate of the nlms algorithm, it is within the

range of 0


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Practical implementation is very similar to that of the lms algorithm. Each iteration

of the nlms algorithm requires these steps in the following order (farhang-

boroujeny 1999, p. 175).

1. The output of the adaptive filter is calculated.

2. An error signal is calculated as the difference between the desired signal and the

Filter output.

3. The step size value for the input vector is calculated.

4. The filter tap weights are updated in preparation for the next iteration.

Tool used. (MATLAB)

MATLAB is a powerful, general-purpose, mathematical software package.

MATLAB possesses excellent graphics and matrix handling capabilities. It

integrates mathematical computing in a powerful language to provide a flexible

environment for technical computing. The salient features ofMATLAB are its in-

built mathematical toolboxes and graphic functions. Additionally, external routines

that are written in other languages such as C, C++, Fortran and Java, can be

integrated with MATLAB applications. MATLAB also supports importing data

from files and other external devices. Most of the functions in MATLAB are

matrix-oriented and can act on arrays of any appropriate dimension. MATLAB

also has a separate toolbox for signal processing applications, which provided

simpler solutions for many of the problems encountered in this research.

The MATLAB software environment suited the needs of this research for thefollowing reasons:

1) The input signals (far-end and near-end talker signals) were voices.These voices were stored as wav files and the wav files were easily imported

into the code. The intermediate signals (echo signals) and output signals

(error signal and Signals obtained after echo cancellation) were obtained as


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wav files. Thus the audio of the voice signals could be literally be heard,

which aided immensely judgments with respect to the results obtained.

2) The signal processing toolbox has in-built functions for almost allsignal processing applications. The toolbox helped the efficiency of the code

since these functions could be called wherever necessary instead of writing

separate sub-routines.

Since MATLAB supports graphics, the results of a simulation could be

represented in a graphical format with ease.


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References :-

y http://en.wikipedia.org/wiki/Adaptive_filtery http://cnx.org/content/m11909/latest/y http://ieeexplore.ieee.org/Xplore/login.jsp?url=http://ieeexplore.ieee.org/iel5/10241/32659/01529581.pdf&authDecision=-203y http://en.wikipedia.org/wiki/Echo_cancellationy http://www.seminarprojects.com/tag/echo-cancellation-using-matlaby http://ylikaaki.homeip.net/Papers/AEC/ACOUSTIC%20ECHO%20CANCELLATION%20USI

NG%20DIGITAL%20SIGNAL%20PROCESSING.pdf

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