A Novel Integer-Bit Estimation Scheme in Digital Filters Based on Probabilistic Behavior of Signals in the Internal Nodes

Accurate estimates of the maximum swing of internal nodes in digital filters are highly desired, which is translated into better implementation on hardware in terms of area, power, and reliability. In this brief, an accurate semi-analytical method for estimating the internal node swing is presented. We use multiple word length method in which the fractional and the integer word lengths are not the same for various nodes. In the proposed method, the probability distribution of signals are considered and, based on that, an accurate evaluation for maximum swing of the internal nodes is provided by using only one simple simulation. This analytical method is confirmed by some theorems on behavior of linear filters that are presented in this brief. Despite most previous methods, our method is independent of the input signal and, thus, the calculated swings are valid for all kinds of inputs. Simulation results for various types of filters such as finite impulse response, DF2, and cascade shows that the approximated range interval by the proposed method is tighter than other methods, which means our proposed method is capable of saving more area and power of digital filters.