An efficient vector-space approach for accurately modeling fixed-point digital signal processors

This paper presents the DSP Software Engineering (DSPSE) Fixed Arithmetic Tool (FAT^TM) method for modeling DSP fixed-point processors and converting an algorithm from a floating-point model to a given DSP fixed-point processor model. All DSP fixed-point processors have associated with them a set of fixed bit length data representations for the storage and manipulation of binary information. We define a vector sub-space for each DSP fixed-point processor, as a direct sum of each distinct fixed bit length data representation sub-space. The direct sum of all DSP fixed-point processor vector subspaces forms a FAT^TM DSP vector space. Furthermore, for our discussion, we define an operator projection to be performed on our DSP vector space such that redundancy in the operational behavior of the DSPs to be modeled can be exploited. In our preferred embodiment we implement the FAT^TM vector space in a C++ environment, resulting in a Fixed Arithmetic C++ Tool (FACT^TM) library for all associated fixed-point DSPs. For our own development we have created, a FACT^TM library for the Texas Instrument TMS320C54x DSP fixed-point processor. The TMS320C54x library has been used in the development of the Japanese Vector Sum Excited Linear Prediction (JVSELP) algorithm and the International Telecommunications Union G.728 standard algorithm