Efficient Computation of Time-Varying and Adaptive Filters

Techniques for efficiently computing digital filters with fixed coefficients, such as distributed arithmetic, achieve great arithmetic savings and are widely used. However, no computationally efficient method of implementing time-varying or LMS adaptive filters exists. We develop two techniques for efficient computation of filters that support time-varying coefficients; these methods are forms of distributed arithmetic that encode the data rather than the filter coefficients. The first approach efficiently computes scalar-vector products, with which a digital filter is easily implemented in a transpose-form structure. This method, based on digit coding, supports time-varying coefficients with no additional overhead. Alternatively, distributed-arithmetic schemes that encode the data stream in sliding blocks support efficient direct-form filter computation with time-varying coefficients. A combination of both of these techniques greatly reduces the computation required to implement LMS adaptive filters.