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Over the past decades a number of new adaptive filter algorithms have been elaborated and applied to meet demands for faster convergence and better tracking properties than earlier techniques could offer. The Filtered LMS algorithm is currently the most popular method for adapting a filter, due to its simplicity and robustness, which have made it widely adopted in many applications. Applications include adaptive channel equalization, adaptive predictive speech coding, Noise Suppression and on-line system identification. Recently, because of the progress of digital signal processors, a variety of selective coefficient update of gradient-based adaptive algorithms could be implemented in practice. Different types of adaptive algorithms have been developed and used in conventional adaptive filters such as, filtered LMS algorithms [1], [2], [3] and [4], filtered X-LMS algorithms [1], [2], [5], and [6], filtered NLMS algorithms and RLS algorithms [1] and [2]. As a result, this chapter surveys sequential filter adaptation techniques and some applications for transversal FIR filter. In other words filters are devices or systems that processes (or reshapes) the input signal according to some specific rules to generate an output signal Figure 1.

The Ultra High Speed LMS Algorithm Implemented on Parallel Architecture Suitable for Multidimensional Adaptive Filtering