“…This optimality can be understood in the sense of Signal-to-Noise Ratio (SNR) maximisation or in the sense of Minimum Mean Squared Error (MMSE, the one used in this chapter), where the optimal LAPTV filter may differ depending on the criterion used. Therefore, LAPTV filters find application in many signal processing areas such as signal estimation, interference rejection, channel equalization, STAP (Space-Time Adaptive Processing), or watermarking, among others (see (Gardner, 1994) and references therein, or more recently in (Adlard et al, 1999;Chen & Liang, 2010;Chevalier & Blin, 2007;Chevalier & Maurice, 1997;Chevalier & Pipon, 2006;Gameiro, 2000;Gelli & Verde, 2000;Gonçalves & Gameiro, 2002;Hu et al, 2007;Li & Ouyang, 2009;Martin et al, 2007;Mirbagheri et al, 2006;Ngan et al, 2004;Petrus & Reed, 1995;Whitehead & Takawira, 2004;2005;Wong & Chambers, 1996;Yeste-Ojeda & Grajal, 2008;Zhang et al, 2006;). This chapter is devoted to the study of LAPTV filters for adaptive filtering.…”