Figure 5: Noise Cancellation. The speech signal to be transmitted (perhaps a mobile phone in a car) is spectrally masked by noise, from, for example a car engine. By using an adaptive filter, we can attempt to minimise the error by fnding the correlation between the noise at the signal microphone and the (correlated) noise at the reference microphone. In this particular the case the error does not tend to zero as we note the signal d(k) = s(k) + n(k) whereas 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 minimising the power of the error signal e(k) we note that only the noise is removed and .e(k) =~ s(k).