An Adaptive filter is a filter that self-adjusts its transfer function according to an optimizing algorithm. Because of the complexity of the optimizing algorithms, most adaptive filters are digital filters that perform digital signal processing and adapt their performance based on the input signal. An Adaptive filter is often employed in an environment of unknown Statistics for various purposes such as system identification, inverse modeling for channel equalization, adaptive prediction and interference canceling. Knowing nothing about the environment, the filter is initially set to an arbitrary condition and updated in a step by step manner towards an optimum filter setting. For updating, the least mean-square algorithm is often used for its simplicity and robust performance. However, the L MS algorithm exhibits slow convergence when used with an ill-conditioned input such as speech and requires a high computational cost, especially when the system to identified has a long impulse response. Adaptive Filtering is an important concept in the field of signal processing and has numerous applications in fields such as Multimedia Applications and communications. Examples in speech processing include speech enhancement, echo and interference cancellation and speech coding. Simulations show that the proposed structure converges faster than both an equivalent full band structure at lower computational complexity and recently proposed SAF structures for a colored input.
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