Active noise cancellation uses a microphone to measure ambient noise and generate an inverted "anti-noise" signal to destructively interfere with and cancel out the noise. It works best for low frequencies while passive noise control using insulation is more effective at higher frequencies. Adaptive noise cancellation algorithms like LMS analyze noise waveforms and generate inverted signals through transducers to reduce perceived noise levels. Noise-cancelling headphones apply this technique to improve listening and sleep on planes by offsetting engine noise.

1. Introduction:
In our increasingly mobile society, individuals are prone to doing just about everything
on the move. Listening to music is certainly not an exception. However, when one listens to
music away from the home, one necessarily has less control over noise exposure. Airplane, bus
and car engines are the most common noise distractions as one travels. Lawnmower engines,
others’ speech and music are also frequently encountered. Surely, there is considerable benefit
in obtaining headphones that could perform active noise cancellation – be able to filter out
noise as one encounters it.
What is Noise Cancellation?
Noise cancellation is an active or passive means of reducing sound emissions, often for
personal comfort, environmental considerations or legal compliance. Active noise control is
sound reduction using a power source. Passive noise control is sound reduction by noise-
isolating materials such as insulation, sound-absorbing tiles, or a muffler rather than a power
source.
Active noise canceling is best suited for low frequencies. For higher frequencies, the spacing
requirements for free space and zone of silence techniques become prohibitive. In acoustic
cavity and duct based systems, the number of nodes grows rapidly with increasing frequency,
which quickly makes active noise control techniques unmanageable. Passive treatments
become more effective at higher frequencies and often provide an adequate solution without
the need for active control.
Adaptive Noise Cancellation (ANC) Method:
Sound is a pressure wave, which consists of alternating periods
of compression and rarefaction. A noise-cancellation speaker emits a sound wave with the
same amplitude but with inverted phase (also known as antiphase) to the original sound. The
waves combine to form a new wave, in a process called interference, and effectively cancel
each other out – an effect which is called destructive interference.

2. Fig. 1: Destructive Interference
Modern active noise control is generally achieved through the use of analog circuits
or digital signal processing. Adaptive algorithms are designed to analyze the waveform of the
background noise, then based on the specific algorithm generate a signal that will either phase
shift or invert the polarity of the original signal. This inverted signal (in antiphase) is then
amplified and a transducer creates a sound wave directly proportional to the amplitude of the
original waveform, creating destructive interference. This effectively reduces the volume of the
perceivable noise.
A noise-cancellation speaker may be co-located with the sound source to be attenuated. In this
case it must have the same audio power level as the source of the unwanted sound.
Alternatively, the transducer emitting the cancellation signal may be located at the location
where sound attenuation is wanted (e.g. the user's ear). This requires a much lower power level
for cancellation but is effective only for a single user. Noise cancellation at other locations is
more difficult as the three-dimensional wave fronts of the unwanted sound and the
cancellation signal could match and create alternating zones of constructive and destructive
interference, reducing noise in some spots while doubling noise in others. In small enclosed
spaces (e.g. the passenger compartment of a car) global noise reduction can be achieved via
multiple speakers and feedback microphones, and measurement of the modal responses of the
enclosure.
Fig. 2: Graphical depiction of active noise reduction

3. Algorithm:
There are several algorithms used to calculate the “anti-noise” signal. The Least Mean
Square (LMS) algorithm is comprised of two processes – a filtering process producing the
output signal and the estimation error, and an adaptive process responsible for the automatic
adjustment of filter tap weights.
Fig. 3: Sample ANC flowchart with LMS
Code in MATLAB:
%noise cancellation
clc;
clear all;
order=2;
size=2; %time duration of inputs
fs=8192; %digital sampling frequency
t=[0:1/fs:size];
N=fs*size; %size of inputs
f1=35/2; %frequency of voice
f2=99/2; %frequency of noise
voice=cos(2*pi*f1*t);
subplot(4,1,1)
plot(t,voice);
title('voice (do not have access to)')
noise=cos(2*pi*f2*t.^2); %increasing frequency
noise

4. %noise=.1*rand(1,length(voice)); %white noise
primary=voice+noise;
subplot(4,1,2)
plot(t,primary)
title('primary = voice + noise (input1)')
ref=noise+.25*rand; %noisy noise
subplot(4,1,3)
plot(t,ref)
title('reference (noisy noise) (input2)');
w=zeros(order,1);
mu=.006;
for i=1:N-order
buffer = ref(i:i+order-1); %current 32
points of reference
desired(i) = primary(i)-buffer*w; %dot product
reference and coeffs
w=w+(buffer.*mu*desired(i)/norm(buffer))';%update coeffs
end
subplot(4,1,4)
plot(t(order+1:N),desired)
title('Adaptive output (hopefully it is close to "voice")')
Fig. 4: Output in MATLAB

5. Application:
It can be used in Noise-cancelling headphones which are headphones that reduce
unwanted ambient sounds using active noise control. This is distinct from passive headphones
which, if they reduce ambient sounds at all, use techniques such as soundproofing.
To cancel the lower-frequency portions of the noise, noise-cancelling headphones
use active noise control. They incorporate a microphone that measures ambient sound,
generate a waveform that is the exact negative of the ambient sound, and mix it with any audio
signal the listener desires.
Drawbacks:
1. Active noise control requires power, usually supplied by a USB port or a battery that
must occasionally be replaced or recharged.
2. Any battery and additional electronics may increase the size and weight of the
headphones compared to regular headphones.
3. The noise-cancelling circuitry may reduce audio quality and add high-frequency hiss,
though reducing the noise may result in higher perceived audio quality.
Conclusion:
Noise cancellation makes it possible to listen to music without raising the volume
excessively. It can also help a passenger sleep in a noisy vehicle such as an airliner. In the
aviation environment, noise-cancelling headphones increase the signal-to-noise
ratio significantly more than passive noise attenuating headphones or no headphones, making
hearing important information such as safety announcements easier. Noise-cancelling
headphones can improve listening enough to completely offset the effect of a distracting
concurrent activity.