A Hierarchical Methodology for Word-Length Optimization of Signal Processing Systems

The problem of converting floating point algorithms to implementation friendly fixed point formats is often solved as an optimization problem where the precision is traded to gain in the implementation cost. The complexity of the problem is known to grow exponentially with more optimizable variables. This paper proposes a divide and conquer technique to solve the growing size of the problem. The approach in this technique is original in the sense that it is formulated from a designers perspective rather than merely attempting to divide and conquer at the algorithmic level. This paper introduces the single noise source model based on which the proposed technique is built. A mixed approach for error propagation is also explained keeping in view of the elements in the circuit that cannot be handled analytically.