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Done By
S . Malki Hussain S.Chand BashaS . Md .Javeed B.Hussain Basha
S.Baba Fakruddin S.Minuddin
Submitted toS . Fouziya Parveen
Goal What is noise ?What is Noise Cancellation ? Simple Idea . Applications Adaptive Filter Adaptive Algorithm( LMS ) Simulation Conclusion
What is noise? Noise consists of unwanted waveforms that can interfere
with communication.
Sound noise: interferes with your normal hearing
.Loud noises
.Subtle noise
.White noise (AWGN)
What is Noise Cancellation?
Noise cancellation is a method to reduce or completely cancel out undesirable sound.
call Active Noise Cancellation .
Noise cancellation tries to 'block' the sound at the source instead of trying to prevent the sounds from entering our ear canals .
These technologies are in their early stages.
The hope is that one day that these technologies can be used to minimize all sorts of unwanted sounds around us
Simple Idea
Cancellation processes depend on simple principle
adding two signals with the same
amplitude and opposite phase the result will be zero signals.
(H)
Adaptive Noise Cancelling Adaptive noise cancelling
- An approach to reduce noise based on reference noise signals
- System output
- The LMS algorithm
K
kktnkwtntstu
1 10 )()()()()(
)()()( 1 ktntukw
Adaptive filter
nonlinear and time-variant .
adjust themselves to an ever-changing environment .
changes its parameters so its performance improves through its surroundings.
Adaptive Filter
Outputsignal
Inputsignal
Adaptive algorithm
Criterion of performance
Filter structure
The coefficients of an adaptive filter change in time
Block diagram of adaptive system
?
Primary
signal
d(n)
N1(n)
Reference
signaly(n)
output
e(n)
adaptive
No(n) S(n)+No(n)
Adaptive algorithm
An adaptive algorithm is used to estimate a time varying signal.
By adjusting the filter coefficients so as to minimize the error.
There are many adaptive algorithms like Recursive Least Square (RLS),Kalman filter,
but the most commonly used is the Least Mean Square (LMS) algorithm.
LMS Adaptive Algorithm
Introduced by Widrow & Hoff in 1959.
Simple, no matrices calculation involved in the adaptation.
In the family of stochastic gradient algorithms.
Approximation of the steepest – descent method
Based on the MMSE criterion.(Minimum Mean square Error)
Adaptive process containing two input signals:
• 1.) Filtering process, producing output signal.
• 2.) Desired signal (Training sequence)
Stability of LMS
The LMS algorithm is convergent in the mean square if and only if the step-size parameter satisfy
Here max is the largest eigenvalue of the correlation matrix of the input data
More practical test for stability is
The LMS Equation
The Least Mean Squares Algorithm (LMS) updates each coefficient on a sample-by-sample basis based on the error e(n).
This equation minimises the power in the error e(n).
The value of µ (mu) is critical.
If µ is too small, the filter reacts slowly.
If µ is too large, the filter resolution is poor.
The selected value of µ is a compromise.
)()()( 1)(nw k nxnenw kk
LMS algorithm Estimates the solution to the Widrow -Hoffequations using gradient descent method which Finds minima by estimatingthe gradient.
X(n)
C(n)
Transversal Filter
LMS
Y(n)
e(n)
d(n)
is the step size
Cont..
e(n)
Adaptive
filter
Unknown
system
X(n)
d(n)
y(n)
filtering operation with theprevious version of the coefficients.
Compare the computed output with the expected output.
Update the coefficients usingthe following computation.
Cont..LMS algorithm
The most widely used real time adaptive filtering algorithm
Convergence speed of the LMS algorithm
Controlled by the spread of eigenvalues of the autocorrelation matrix of the input data
Enhanced by reducing the eigenvalue spread
Conclusion
Active noise cancellation is a method to cancel out undesirable sound in real time
The adaptive filter is used to estimate the error in noisy wave
Many algorithms are used in adaptive filter like LMS RLS & MSE and the better is LMS .