6 - DSP algorithms

Abstract

This chapter discusses the computational properties of digital signal processing systems. Each structure (algorithm) involves a set of basic operations called processes. At the higher levels of the hierarchy, these processes correspond to large digital signal processing (DSP) tasks (for example, FFTs, DCTs, and digital niters) while the lowest level processes involve arithmetic operations. The computational properties of the algorithms at the different hierarchical levels limit system performance. Properties of interest are the order of execution of the arithmetic operations (processes), the number of operations that can be executed in parallel, and the shortest possible execution time. The computational properties of higher-level processes can be analyzed in a manner similar to arithmetic operations. The chapter also discusses a formal method to derive the difference equations in a computable order from the signal-flow graph. In this form, the set of difference equations can be translated directly into code for a standard signal processor or a multicomputer. To avoid dangerous pitfalls, it is necessary to use a design method that guarantees the integrity at each design step involved in transforming the DSP algorithm into a working system.