Low Hardware Complexity Pipelined Rank Filter

Fast median calculation method

“…Multiple architectures can be derived with different tradeoffs between area and time in fully pipelined structures. 3 Estimated ratio of T [5] /T for critical paths of the architecture in [5] (T [5] ) against the critical path of the architecture in Figure 1 (T) as a function of window size N. …”

“…A rank filter: An order R filter, for a set of N elements has R elements less or equal to the output and N -R elements greater or equal to the output [5]. For N = 2k +1, the median is a rank filter with R = k. The method in this Letter calculates the median by setting P = R + 1 initially.…”

“…Non-sorting based methods, especially those designed for hardware architectures achieve the calculation in a number of steps related to the bit length of unsigned integers, W, rather than N [4]. The method of Prokin and Prokin [5] However, no previous known method operates on more than 1-bit at a time, as presented here. The data representation of B-bit slices is changed on the fly allowing the method to explore ahead, further than one bit a time, using a Quantum Representation (QR) of bits, which retains the advantages of flexible data manipulation and data parallel properties.…”

“…Figure 3 shows that this does not happen for N >7. The median computation time in [5] is t [5] = WT [5] and, for figure 1, t = (W/B)T, thus the speedup factor of Figure 1 is s = B(T [5] /T) with T [5] and T representing the critical paths of [5] and Figure 1 respectively. At N = 15, directly from Figure 3, T [5] /T ~ 0.625 for B = 2, and consequently speedup s = B(T [5] /T) ~ 1.25 or 25% faster.…”

“…T is essentially due to the CSA tree followed by a chain of 2 B -1 accumulators of log 2 N width each, which make them suitable for implementation with fast full carry look-ahead adders [7]. T [5] is basically the delay cost of the CSA tree.…”