correlation function is a measure of how statistically similar two functions are. The autocorrelation function of a random signal is defined as the expectation of a signals value at time n multiplied by its complex conjugate value at a different time m. This is shown in equation (3.1), for time arbitrary time instants, n and m. _xx (n,m)=E[x(n) x^* (m) ] ..(3.1) As this thesis deals only with real signals the above equation becomes._xx (n,m)=E[x(n)x(m)]The derivations of adaptive filtering algorithms utilize the autocorrelation matrix, R. For real signals this is defined as the matrix of expectations of the product of a vector x(n) and its transpose. This is shown in equation (3.2) [21]. R=[((E[|x_0 (k)^2 | ] &E[x_0 (k) x_1 (k) ] ?&E[x_0 (k) x_N (k) ] )@(E[x_1 (k) x_0 (k) ]&E[|x_1 (k)^2 | ] ? &E[x_1 (k) x_N (k) ]@?&?&?@E[x_N (k) x_0 (k) ]&E[x_N (k) x_1 (k) ] ?&E[|x_N (k)^2 | ] ))] R=E[x(k)x^T (k)] (3.2)The autocorrelation matrix has the additional property that its trace, i.e. the sum of its diagonal elements, is equal to the sum of the powers of the values in the input vector by Farhang-Boroujeny [15].