Interband Alias-Free Subband Adaptive Filtering with Critical Sampling

Adaptive Filtering is an important concept in the field of signal processing and has numerous applications in fields such as speech processing and communications. 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 toward an optimum filter setting. For updating, the least meansquare algorithm is often used for its simplicity and robust performance. However, the LMS 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 be identified has a long impulse response. To overcome the limitations of a conventional full band adaptive filtering, various sub band adaptive filtering (SAF) structures have been proposed. Properly designed, an SAF will converge faster at a lower computational cost than a full band structure. However, its design should consider the following two facts: the inter band aliasing introduced by the down sampling process degrades its performance, and the filter bank in the SAF introduces additional computational overhead and system delay. In this project, a critically sampled SAF structure that is almost Alias-free is proposed to reap all the benefits of using an SAF. Since the proposed SAF is performed using subbands that is almost alias-free, there is little inter band aliasing error at the output. In each sub band, the inter band aliasing is obtained using a bandwidth-increased linear-phase FIR analysis filter, whose pass band has almost-unit magnitude response in the subband interval, and is then subtracted from the sub band signal. This aliasing cancellation procedure, however, causes the spectral dips of the sub band signals. These spectral dips can be reduced by using a simple FIR filter. 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. The analysis is done using MATLAB, a language of technical computing, widely used in Research, Engineering and scientific computations.