Automatic Floating-Point to Fixed-Point Transformations

Many digital signal processing and communication algorithms are first simulated using floating-point arithmetic and later transformed into fixed-point arithmetic to reduce implementation complexity. For the floating-point to fixed-point transformation, this paper describes two methods within an automated transformation environment. The first method, a gradient-based search for single-objective optimization with sensitivity information, provides a single solution, and can become trapped in local optima. The second method, a genetic algorithm for multi-objective optimization, provides a family of solutions that form a tradeoff curve for signal quality vs. implementation complexity. We provide case studies for an infinite impulse response filter. In the case study, implementation complexity is lookup table area for a field programmable gate array (FPGA) realization. We have made the transformation methods available in a software release on the Web.