Accurate and Efficient Implementations of Recursive Filtering based on SIMD and Cascaded Form

Implementation of recursive filtering based on parallel computation on SIMD is more difficult than non-recursive filtering due to data dependency. To that end, this paper proposes an efficient algorithm for computing the recursive equation by transferring the data dependency from individual samples to multiple blocks of samples. Our algorithm is proposed based on cascaded forms; It will be illustrated that the recursive filter built by cascaded forms can deal with the rounding error issue in some filter design. The performance evaluation results of our algorithms are presented not only by the number of instructions but the real spent clock cycles. The throughput of our algorithm is tested on different types of micro-architecture with data rates approaching 260 MHz.