Before moving to the actual adaptive filtering problem, we need to solve the optimum linear filtering problem (particularly, in the mean-square-error sense). We start by explaining the analogy between linear estimation and linear optimum filtering. We develop the principle of orthogonality, derive the Wiener–Hopf equation (whose solution lead to the optimum Wiener filter) and study the error surface. Finally, we applied the Wiener filter to the problem of linear prediction (forward and backward).
KeywordsMean Square Error Linear Prediction Infinite Impulse Response Wiener Filter Finite Impulse Response Filter
- 1.A.H. Sayed, Adaptive Filters (John Wiley& Sons, Hoboken, 2008)Google Scholar
- 2.S. Haykin, Adaptive Filter Theory, 4th edn. (Prentice-Hall, Upper Saddle River, 2002)Google Scholar
- 3.G.H. Golub, C.F. van Loan, Matrix Computations (The John Hopkins University Press, Baltimore, 1996)Google Scholar
- 4.B.D.O. Anderson, J.B. Moore, Optimal Filtering (Prentice-Hall, Englewood Cliffs, 1979)Google Scholar
- 5.T. Kailath, A.H. Sayed, B. Hassibi, Linear estimation (Prentice-Hall, Upper Saddle River, 2000)Google Scholar