Computing methods for signal algebra operators: A DSP core implementations approach

This document presents a methodology based on a signal algebra operator theoretic approach for the mathematical formulation of signal processing algorithms and efficient systematic procedures for mapping these algorithms to target hardware computing structures through iconic and functional programming techniques, and automatic core generation efforts. An algorithm development and implementation environment is described in this work as a central theme in studying DSP computing methods. This environment is an aggregate of the following items: a PC Workstation platform, MATLAB® tools, digital signal processing (DSP) microprocessor units, and field programmable gate array (FPGA) units. Special emphasis is given to the concepts of modularity and scalability during a hardware implementation. A main goal of this on going work is to establish formal links amongst the elements of the environment in order to assist in reducing the algorithm development and implementation time-line. The results presented here center on the formulation of a methodology for computing methods as an operator theoretic approach to the digital processing of signals, and on the study of the computing hardware structure and overall architecture of floating point DSP microprocessor units and FPGAs for the implementation of complex fast Fourier transform (FFT) cores. The new methodology presented in this work was successfully utilized for the generation of signal processing cores for DSP and FPGA hardware units in a signal algebra setting, with advantages such as improved latency time, and modular and reconfigurable features, which make the developed cores desirable for the implementation of more advanced digital signal processing applications.