A Mathematical framework for Parallel computing of discrete-time discrete-frequency transforms in Multi-core Processors

This paper presents a mathematical framework for a family of discrete-time discrete-frequency transforms in terms of matrix signal algebra. The matrix signal algebra is a mathematics environment composed of a signal space, a finite dimensional linear operators and special matrices where algebraic methods are used to generate these signal transforms as computational estimators. The matrix signal algebra contribute to analysis, design and implementation of parallel algorithms in multi-core proccesors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB^® with the Parallel Computing Toolbox^™. We found that there is advantage to use multi-core processors and a parallel computing environment to minimize the high execution time. Also, speedup and efficiency increases when the number of logical processor and length of the signal increase. Moreover, a superlinear speedup is obtained in this experimental investigation.