Distributed arithmetic based recursive digital filter designs for high throughput applications

The design problem of high speed recursive digital filters, particularly for real time applications, is addressed in this paper. Recursive digital filters have been widely used in many important applications. These include the cases such as AR filters, Kalman filters and adaptive filters. Recursive filters are sequential in nature, which often becomes the performance bottleneck in real time applications. Conventional speed up techniques such as pipelining and parallel processing are not directly applicable unless an expensive "look-ahead" transform is employed first to add congruency to the recursive computing. This, nonetheless, will increase the hardware complexity drastically. In this paper, we propose a new design scheme which is based on the principle of distributed arithmetic (DA). The DA approach tries to exploit parallelism at bit level and can effectively improve the throughput rate of the filter without resorting to the look ahead transform as in the bit-parallel designs. For those high order recursive filter designs, we further propose a decomposition scheme to minimize complexity. To demonstrate this new scheme, a four-tap recursive AR filter design is also given in this paper.