  In many application of noise cancellation, the changes in signal
characteristics could be quite fast. This requires the utilization of adaptive
algorithms, which converge rapidly. Least Mean Squares (LMS) and Normalized
Least Mean Squares (NLMS) adaptive filters have been used in a wide range of
signal processing application because of its simplicity in computation and
implementation. The Recursive Least Squares (RLS) algorithm has established
itself as the "ultimate" adaptive filtering algorithm in the sense that it is
the adaptive filter exhibiting the best convergence behavior. Unfortunately,
practical implementations of the algorithm are often associated with high
computational complexity and/or poor numerical properties. Recently adaptive
filtering was presented, have a nice tradeoff between complexity and the
convergence speed. This paper describes a new approach for noise cancellation
in speech enhancement using the two new adaptive filtering algorithms named
fast affine projection algorithm and fast Euclidean direction search algorithms
for attenuating noise in speech signals. The simulation results demonstrate the
good performance of the two new algorithms in attenuating the noise.

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