International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
ISSN 2319 - 4847
Special Issue for National Conference On Recent Advances in Technology and
Management for Integrated Growth 2013 (RATMIG 2013)
LEAST MEAN SQUARE (LMS) ADAPTIVE FILTER FOR
NOISE CANCELLATION
1
Prof. Vaishali M. Karne
G.N.I.E.T, Nagpur, India
v.karne03@gmail.com
2
Prof. Akhilesh Singh Thakur
M.TECH [ Electronics and communication]
G.G.I.T.M, Bhopal, India
akhilesh.thematrix@gmail.com
3
Dr. Vibha Tiwari
Ph.D [ Electronics and communication]
ecggitm@gmail.com
Abstract
In the field of Digital Communication & signal processing, signals are associated with noise and distortions. This is due to the
fact that system undergoes the time varying physical process which are unknown sometime. These variations can be
eliminated using adaptive filtering as it senses the unknown variation in the signal properties. Finite impulse response (FIR)
and Infinite impulse response (IIR) filters are available for adaptation process. amongst both of them FIR is widely used
adaptive filter. The approaches of adaptation can be achieved by least mean square (LMS), wiener filter, recursive least
squares filter (RLS) etc. LMS is the best suited filter for adaptive filter in noise cancellation and many other applications.
Noise cancellation can be achieved by using proper value of the parameters. In this paper the performance of LMS filter is
used for noise cancellation in voice signal. The step size (µ) is considered to be the parameter where we can make the
changes.
Keywords: LMS adaptive filter (least mean square), FIR (finite impulse response), IIR (infinite impulse response),
Step size.
1. INTRODUCTION
In number of applications, including biomedical engineering, radar, sonar and digital communications, the main aim
is to identify and separate a useful signal corrupted due to interference and noise. The most familiar method of
figuring and computing a signal corrupted by additive noise’ is to allow it to pass through the filter which will aim to
suppress the noise without changing the signal. Filters that can be used for the following purpose are fixed or
adaptive. Fixed filters are designed with the knowledge of signal as well as noise. On the other hand Adaptive
filters, are capable of adjusting automatically the parameters, and the design does not requires knowledge of
previous signal or noise characteristics. Noise cancellation is a contrast of optimal filtering which is advantageous
in many other applications. The reference input which is derived from the noise field are used where the signal is
poor or unpredictable. This extracted input is then filtered and deducted from the initial input containing signal and
noise both. The resulting initial noise is extenuate or discard by noise cancellation
As compared to the conventional filter design techniques, adaptive filters does not consist of constant filter
coefficients and previous information is also unknown. Thus the filter with adjustable parameters is known as
adaptive filter. Adaptive filter self adjusts their coefficients to minimize the error signal, which can be accomplished
as finite impulse response (FIR), infinite impulse response (IIR), lattice and transform domain filter. LMS filter is
the simplest one as it minimizes the instantaneous square error and simple gradient-based optimization method [5].
Among all the other algorithms, the Least Mean Square (LMS) algorithm is most suitable for the adaptation of the
Organized By: GNI Nagpur, India
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
ISSN 2319 - 4847
Special Issue for National Conference On Recent Advances in Technology and
Management for Integrated Growth 2013 (RATMIG 2013)
filter coefficients. Thus, the objective of operating under changing conditions and readjust itself continuously to
minimize the error is fulfilled by the LMS algorithm [8].
There are various parameters related to signal processing including step size, hopping parameter and proper use of
random noise signal, etc. Further working on this parameter we can minimize noise and proper use of such
parameters helps in noise cancellation.
Adaptive filtering is now being used in many signal processing application areas such as:
1. System Identification
2. Signal control
3. Echo cancellation
4. Signal prediction
5. Adaptive feedback cancellation
6. Noise cancellation
7. Communications, etc. [6] [9].
In this paper we are more concentrated on noise cancellation which will be achieved by the Adaptive filter using
LMS algorithm. The distinct values cannot be expected from LMS algorithm, but it does promise for the mean
convergence. Thus even if the weights are varied by a small amount, optimal weights are affected. However mean
would be inaccurate, if the variance is large. It is because of not choosing the proper value of step size µ.step size
can decrease the steady-state error, but the convergence rate will be poor. A larger step size can speed up the
convergence rate, but at the same time it increases the steady-state error [4]. Step adjustment strategy of the
algorithm is advanced to some extent, but the step changes sharply when the algorithm error approximate zero, as
may increase the steady-state error [10] but further variation in the step size can improve the above mentioned error.
Conclusively it will result in reduction of noise.
This paper is organized as follows, in section (2) explains about the LMS Adaptive Filter. Section (3) explains about
the Noise Cancellation, (4) proposed LMS adaptive filter for noise cancellation, (5) Provides the simulation results,
(6) gives software simulation of design, (7) the future scope is discussed and (8) provides the conclusion.
2.LMS ADAPTIVE FILTER
LMS adaptive filter is used world wide because of its easy computation and flexibility. This algorithm [2] is a
member of stochastic gradient algorithm , and because of its robustness and low computational complexity it is used
worldwide. The algorithm using the steepest distance [2] is as given below.
W (n+1) =w (n)-µ J (W (n))
(1)
J (W (n)) =-2pdx+2Rxw (n)
(2)
Where
Rx and pdx are the instantaneous estimates and are defined as
Rx x (n) xT (n), pdx d (n) x (n)
(3)
Substituting equation (1) and (2) in the above equation we get
W (n+1) = w (n)+2µe(n)x(n)
(4)
Where
Organized By: GNI Nagpur, India
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
ISSN 2319 - 4847
Special Issue for National Conference On Recent Advances in Technology and
Management for Integrated Growth 2013 (RATMIG 2013)
Y (n) =WT (n) x (n)
.
(5)
E (n) = d (n)-y (n)
(6)
The above two equations are required output of LMS algorithm where y (n) is the filter output and e (n) is the error.
Figure below shows the block diagram of [12] adaptive filter
Figure (1) A Typical Adaptive filter block diagram
If the values of d (n) and y (n) will become equal we will get zero error. This filter could be used in combination of
various other applications discussed above but our main focus is on noise cancellation.
There are number of parameters related to LMS adaptive filter, which could differently play an important role in
order to reduce the error. Various applications are also there, which are already discussed above can also be
analyzed using LMS filter. In this paper noise cancellation is achieved by variation in LMS algorithm, i.e. step size.
LMS adaptive filter also deals with the problem of Adaptive Noise Cancellation (ANC) for signal corrupted with
an additive white Gaussian noise.
3. NOISE CANCELLATION
Noise cancellation is a scheme of figuring out signals corrupted by additive noise or interference. From the figure
[13] given below it is clear that this system is comprised of primary as well as reference input. Input to the primary
one is Signal source and indirectly noise source as well, Input to the reference one is Noise source.
Figure (2) Adaptive Noise Canceller
From [13] the output (z) can be analyzed which is a combination signal and noise with adaptive filter. This can be
analyzed from the following equations [13].
Organized By: GNI Nagpur, India
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
ISSN 2319 - 4847
Special Issue for National Conference On Recent Advances in Technology and
Management for Integrated Growth 2013 (RATMIG 2013)
z = s + n0-y
(1)
Squaring both the side we get
z2= s2 + (n0- y)2 + 2s (n0- y)
(2)
Taking expectations (3) of both sides and realizing that s is uncorrelated with n0 and with y, yields
E[z2]=E[s2]+E[(n0-y)2]+2E[s(n0-y)]
=E [s2] +E [(n0-y)2 ]
The signal power E [s2] will be unaffected as the filter is adjusted to minimize E [z2]. Accordingly, the minimum
output power is
min E [z2]= E[s2]+min E[(n0-y)2]
(4)
Thus When the filter is adjusted so that E [z2] is minimized, E [(n0-y)2 ] is, therefore, also minimized. The filter
output y is then a best least squares estimate of the primary noise no. Moreover, when E [(n0-y)2] is minimized,
[(z -s)2] is also minimized,
Therefore (z -s) = (n0- y).
(5)
Adjusting or adapting the filter to minimize the total output power is thus tantamount to causing the output z to be a
best least squares estimate of the signal s for the given structure and adjustability of the adaptive filter and for the
given reference input. The output z will contain the signal s plus noise. The output noise is given by (n0 -y). Since
minimizing E [z2] minimizes E [(no - y)2] minimizing the total output power minimizes the output noise power.
Since the signal in the output remains constant, minimizing the total output power maximizes the output signal-tonoise ratio.
Noise cancellation can be achieved by various other methods, as we have reviewed that step size variation plays an
important role for noise cancellation. Other parameters are also associated which can be adjusted in order to achieve
noise cancellation. Next we will discuss proposed methods for the same.
4.PROPOSED LMS ADAPTIVE FILTER FOR NOISE CANCELLATION
In this paper we have proposed generated voice signal with voice=cos2Πf1t. This voice is corrupted by noise &
noise = cos (2Πf1t. ^2). This signal is mixed with noise and need to be repaired while reception but we are familiar
with AWGN (Additive white Gaussians noise) which is a random known noise. We will again mix our signal with
random noise with random noise ref=noise+.25*rand. Now the signal seems to be corrupted with noise as well as
noise is random in nature. Such type of uncertainty and variation can be sensed by LMS adaptive filter . The LMS
filter can work in many different ways by working on different parameters. In this paper we are concentrating on
step size µ. In our proposed paper value of µ is selected to be ( 0.006) and the changes we made is by corrupting the
signal not only with noise but the random noise is also introduced and the signal nearest to the original signal is
generated. The simulated results are shown below.
Organized By: GNI Nagpur, India
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
ISSN 2319 - 4847
Special Issue for National Conference On Recent Advances in Technology and
Management for Integrated Growth 2013 (RATMIG 2013)
5.SIMULATION RESULT
The program in this proposed paper is written on MATLAB. Figure below shows the simulation results and various
waveforms of associated signals. The first waveform shows the voice signal generated of amplitude (A=1) and time
period (T=2). Second waveform shows the noise generated i.e. noise wits voice of same time period and amplitude
(A=2). Again the same signal is mixed with random noise which is shown in third waveform. After applying LMS
algorithm the resultant signal is produced which is close to the original signal.
voice signal
1
0
-1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
primary = voice + noise (input1)
1.6
1.8
2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
reference (noisy noise) (input2)
1.6
1.8
2
0
0.2
0.4
0.6
1.4
1.6
1.8
2
0
0.2
0.4
0.6
1.4
1.6
1.8
2
2
0
-2
2
0
-2
0.8
1
1.2
Adaptive output voice
2
0
-2
0.8
1
1.2
Figure (3) Simulation result.
6. SOFTWARE SIMULATION OF DESIGN
In order to work on Noise cancellation with less error, the Adaptive filter must be designed with proper Digital
Signal Processing. It will be achieved using MATLAB. It gives an easy approach for designing and help throughout
the programming for the beginners as well. MATLAB software is the best suited software for filters. Programming
in the proposed paper as well as the simulation is done on MATLAB.
7. FUTURE SCOPE
For proper functioning of the filter we can make the changes in the filter itself, by choosing the type of filter and the
order of the Filter. As the noise cancellation is done on voice signal, it can also be achieved in various applications
where the pure form of signal is required. ECG and EEG are such examples. In the proposed paper the value of step
Organized By: GNI Nagpur, India
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
ISSN 2319 - 4847
Special Issue for National Conference On Recent Advances in Technology and
Management for Integrated Growth 2013 (RATMIG 2013)
size is (µ=0.006), which can also be changed but the result be different from the nearest value of the original signal.
We can even make the changes in order of step size rather than making changes in step size which can reduce the
steady state error as it is always observed while changing the step size.
8. CONCLUSSION
Based on the mathematical solutions and the Adaptive filter theory we have proposed adaptive filter design and an
algorithms for noise cancellation. With the variation in step size as in noise are reduced but steady state error
increases. At the same time in the Algorithm itself we can make changes, by changing the values of parameters
separately or combine. After getting required simulation results the values are finalized. The value of step size
chosen to be best suited for the original signal to be generated.
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Organized By: GNI Nagpur, India
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
ISSN 2319 - 4847
Special Issue for National Conference On Recent Advances in Technology and
Management for Integrated Growth 2013 (RATMIG 2013)
[15] Yonggang Yan, Junwei Zhao (lCCASM 2010) “An Novel Variable Step Size LMS Adaptive Filtering
Algorithm Based on Hyperbolic Tangent Function” (lCCASM 2010)
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