1.
BITS Pilani
Pilani Campus
EEE G529T PART 1
ANC LMS SINGLE TONE MATLAB
Vikas Kalwani
EEE Department
BITS Pilani, Pilani

2.
BITS Pilani, Pilani Campus
ACTIVE NOISE CONTROL
Why do we need Noise Control?
 Noise control is a very important aspect of modern engineering systems
 In aircrafts, control on the engine noise is a must for the Air Traffic Industry to Flourish
 In the offices of MNC’s that work in the urban Residency amidst traffic and industrial
noises, Noise control is essential
 Also, many biological problems due to Noise when uncontrolled
Types of Noise Control
ACTIVE PASSIVE
• Uses Active devices
• Efficient at low frequencies
• Selective Filtering
• Less Bulky
• Uses Passive elements like
Thermocol etc. to block the path of
the noise thereby attenuating it

3.
BITS Pilani, Pilani Campus
BASICS
Primary Input -> Signal s + Noise n
The Noise is not correlated to the signal
Reference Input -> Noise that is correlated to the noise present in the primary signal.
Reference signal can be recorded near the noise source or when the signal is not present.
 The Reference Input is filtered by the Adaptive filter to ŋ which is a close approximate to the
noise in the primary input . The filtered output ŋ is subtracted from the primary input to produce
the System Output. The adaptive algorithm updates the filter coefficients of the filter based on
this System Output. The Output is processed by the LMS Algorithm which in turn changes the
weights of the filter.
NOTE
Useful signal s is uncorrelated with n and ŋ.
E[sn]=0 and E[sŋ]=0

4.
BITS Pilani, Pilani Campus
 Subtracting noise from a signal involves the risk of distorting the signal and if done
improperly, may lead to increase in the noise level. So, the noise estimate ŋ should
be an exact copy of n
 characteristics of the transmission paths are unknown and unpredictable, filtering
and subtraction are controlled by an adaptive process. Hence, an adaptive filter
capable of adjusting its impulse response to minimize an error signal (which
depends on the filter output) is used.
 Error Signal/System Output is minimized using LMS, RLS, NLMS and other
algorithms

5.
BITS Pilani, Pilani Campus
ADAPTIVE NOISE CANCELLER
In noise canceling systems the objective is to produce a system output ŝ = s + n -
ŋ that is a best fit in least square sense to signal s. This is done by feeding the
system output back to the adaptive filter and adjusting the filter through
adaptive algorithm to minimize total system output power i.e. system output
serves as error signal for adaptive process.

6.
BITS Pilani, Pilani Campus
ŝ = s + n – ŋ
ŝ2 = s2 + (n – ŋ)2 + 2s(n – ŋ)
• Taking expectations on both sides,
E[ŝ2]= E[s2]+ E[(n – ŋ)2] + E[2s(n – ŋ)]
• Realizing that s is uncorrelated to n and ŋ, E[2s(n – ŋ)]=0
E[ŝ2]= E[s2]+ E[(n – ŋ)2]
• The signal power E[s2] remains unaffected as the filter is adjusted to minimize
E[ŝ2]
min(E[ŝ2])= E[s2]+ min(E[(n – ŋ)2])
• As signal power is fixed and noise power of the output is getting reduced,
we get higher signal to noise ratios
To be minimized
E[x2(t)] = RMS POWER
NOISE CANCELLATION
Signal power

7.
BITS Pilani, Pilani Campus
LMS ALGORITHM

8.
BITS Pilani, Pilani Campus
SIMULATION AND RESULTS
LMS Algorithm was implemented successfully. The following graphs describe it.
TIME DOMAIN REPRESENTATION
R=10 (Repetitions)
I=50000 (Iterations)
L=5 (Length)
N=4 (Order)
u=0.002 (Step Size
Parameter)
PARAMETERS

9.
BITS Pilani, Pilani Campus
SIMULATION AND RESULTS
Mean Square Error (dB)
The MSE reduces by a margin
of 25 dB. We can have a
faster reduction in MSE by
increasing the value of step
Size parameter u.

10.
BITS Pilani, Pilani Campus
VARIATION IN PARAMETERS
VARIATION IN NUMBER OF ITERATIONS
I=10000 I=50000
Noise Source Signal
v = 0.8*randn(I,1);
More reduction in MSE when the number of Iterations are large
[MSE(dB)]10000 = -20.64 dB [MSE(dB)]50000 = -27.27 dB

11.
BITS Pilani, Pilani Campus
VARIATION IN PARAMETERS
VARIATION IN NUMBER OF ITERATIONS
I=10000 I=50000
Noise Source Signal
v = 0.6*randn(I,1);
More reduction in MSE when the number of Iterations are large
[MSE(dB)]10000 = -13.71 dB [MSE(dB)]50000 = -27.27 dB
u=0.0002

12.
BITS Pilani, Pilani Campus
VARIATION IN PARAMETERS
VARIATION IN LENGTH OF ADAPTIVE FILTER
L=5 L=10
Noise Source Signal
v = 0.8*randn(I,1);
More reduction in MSE when length of the AF is larger
[MSE(dB)]5 = -29.72 dB [MSE(dB)]10 = -40.28 dB
u=0.0002
I=50000

13.
BITS Pilani, Pilani Campus
VARIATION IN PARAMETERS
VARIATION IN STEP SIZE PARAMETER
u=0.0002
Noise Source Signal
v = 0.8*randn(I,1);
Quicker reduction in MSE when u is larger
[MSE(dB)]5 = -29.72 dB [MSE(dB)]10 = -29.23 dB
I=50000
L=5
u=0.001

14.
BITS Pilani, Pilani Campus
ANC has been done for Single Tone Signal here.
Real Test begins, when the signal is a speech signal.
For that we will use the LMS Block in the Data
Acquisition Toolbox of Matlab.