A unified approach to transform domain LMS adaptive filtering

The authors present a generalized structure for a transform-domain least-mean-square (LMS) adaptive algorithm. In this structure, different transforms, including the Fourier transform, can be presented and used to improve both convergence and estimation over time-domain processing. The structure is general in the sense that it uses information in a successive time data blocks for each iteration in the transform domain. Further, it uses all values of the input transform to estimate each value of the desired transform. The generalized structure, therefore, accounts for nonGaussian processes as well as processes with slowly decaying correlation functions. Previously introduced structures, such as frequency-domain LMS, are special cases of the introduced structure and they result for specific time-varying environment. These can also be special cases obtained by setting some of the structure weights to zero values prior to processing. A mean-square error analysis is provided.<>