A Projection Approach to Adaptive Ifir Filtering

Current adaptive interpolated finite impulse response (IFIR) filtering algorithms update the interpolation filter and the model filter separately while in each case the other filter is fixed. In contrast, we modify the standard least mean squares (LMS) algorithm such that after each iteration the adapted filter is projected back into the set of IFIR filters. This can be considered a joint update of the interpolation filter and the model filter. We also propose a simplified version of our new algorithm. With K and D denoting the lengths of the model and the interpolation filter, respectively, the complexity of our new simplified projected LMS algorithm is only O(K+D) flops per iteration. Normalized variants of the new algorithms are derived as well. The performance of the new simplified normalized algorithm is compared in two numerical examples with a current state-of-the-art adaptive IFIR filtering algorithm. We find that our new algorithm converges faster. At the same time, our algorithm does not require experimental tuning of the step size.