Transformational Design of Digital Signal Processing Applications

In the design of modern digital systems, such as image processing systems, it is, because of their complexity, of great importance that correctness is guaranteed during the design. Transformational design is a method that integrates guaranteed correctness into the design process. Correctness-by-construction is obtained by applying local behavior-preserving transformations —which have themselves already been proven correct— to derive an implementation from a specification. Essential to the transformational design method are design representations which have formal semantics, in order to prove the behavior-preserving property of transformations. Also, it is significantly simplified when a single design representation language is used during the complete synthesis trajectory. Flow graph languages, as demonstrated by their application in many high-level synthesis tools, are good candidates for such representations. At the University of Twente, TRADES1 (Transformational Design System) is being developed. In addition to the design of full-scale DSP applications the system is targeted as a preprocessor for silicon compilation systems, such as Phideo (Philips Research). The system is built around the single-token signal flow graph language SIL2. A formal model for SIL is developed and used to prove the correctness of transformations. The feasibility of transformational design based on SIL is illustrated by an example design of a first-order IIR filter.