This dissertation was presented to the Faculty of the Graduate School of The University of Texas at Austin in partial fulfillment of the requirements for the degree of

Ph.D. in Electrical Engineering

**Abstract**

**Automating Transformations from
Floating-point to Fixed-point for
Implementing Digital Signal Processing Algorithms**

Kyungtae Han, Ph.D.E.E.

The University of Texas at Austin, August 2006

Supervisor:

Prof.
Brian L. Evans

Dissertation - Defense Slides - Software - Wordlength Optimization

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. This transformation process may take more than 50% of the design time for complex designs. In addition, wordlengths in fixed-point designs may be altered at later stages in the design cycle. Different choices of wordlengths lead to different tradeoffs between signal quality and implementation complexity.In this dissertation, I propose two methods for characterizing the trade offs between signal quality and implementation complexity during the transformation of digital system designs to fixed-point arithmetic and variables. The first method, a gradient-based search for single-objective optimization with sensitivity information, scales linearly with the number of variables, but can become trapped in local optima. Based on wordlength design case studies for a wireless communication demodulator, adding sensitivity information reduces the search time by a factor of four and yields a design with 30% lower implementation costs.

The second method, a genetic algorithm for multi-objective optimization, provides a Pareto optimal front that evolves towards the optimal tradeoff curve for signal quality vs. implementation complexity. This second method can be used to fully characterize the design space.

I propose to use wordlength reduction methods of signed right shift and truncation to reduce power consumption in a given hardware architecture. For each method, I derive the expected values of the number of gates that switch during multiplication of the inputs. I apply the signed right shift method and the truncation method to a 16-bit radix-4 modified Booth multiplier and a 16-bit Wallace multiplier. The truncation method with 8-bit operands reduces the power consumption by 56% in the Wallace multiplier and 31% in the Booth multiplier. The signed right shift method shows a 25% power reduction in the Booth multiplier, but no power reduction in the Wallace multiplier.

Finally, this dissertation describes a method to automate design assistance for transformation from floating-point to fixed-point data types. Floating-point programs are converted to fixed-point programs by a code generator. Then, the proposed wordlength search algorithms offer designers the freedom to determine data wordlengths to optimize the tradeoffs between signal quality and implementation complexity.

For more information contact: Kyungtae Han <kt.han4u@gmail.com>