Adaptive algorithm –The aim of adaptive algorithm is to adapt the filter coefficients such that the mean square error between the desired signal and input signal to filter is close to zero as possible. Many possible filter update algorithms exist and one of the most computationally efficient of these is the least mean square algorithm. Adaptive noise canceller is shown in figure below, the speech signal to be transmitted (perhaps a mobile phone in a car) is spectrally masked by noise, for example a car engine. By using an adaptive filter, we can attempt to minimize the error by finding the correlation between the noise at the signal microphone and the (correlated) noise at the reference microphone. In this particular case the error does not tend to zero as we note the signal d (k)=s(k)+n(k) where as the input signal to the filter is x(k)=n(k) and does not contain any speech. Therefore it is not possible to “subtract" any speech when forming e (k) = d (k)-y (k). Hence in minimizing the power of the error signal e (k) we note that only the noise is removed and e (k) ~s (k).

The LMS Algorithm

Initialization
K=1
Wk=0
0>µ<1
Y(k)=WT (k)x(k)
E(k)=d(k)-Y(k)
W(k+1)=W(k)+2µe(k)x(k)
Loop1