Reyes-Rodriguez, Violeta

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    Study of accuracy and hardware performance in discrete transforms and their fast algorithms
    (2015) Reyes-Rodriguez, Violeta; Jiménez-Cedeño, Manuel; College of Engineering; Santiago, Nayda; Rodriguez, Domingo; Department of Electrical and Computer Engineering; Molina, Omar
    Nowadays, during the design of digital arithmetic units, most research efforts are centered in finding algorithms that reduce resource consumption or latency. Efforts to find algorithms that provide higher accuracy are scarce. This thesis presents a study of accuracy and hardware performance of discrete transforms and their fast algorithms. The discrete transforms studied included the Fourier (DFT), the Hartley (DHT), and the cosine (DCT) direct algorithms. The fast DFT treatments were the Cooley-Tukey and Pease. The fast DHT treatments included the Bracewell and Hou. In the case of the DCT the fast treatments evaluated were the Nikara and Translation. This work used approximation and statistical methods for the accuracy analysis. These methods quantify the normwise relative error of the discrete transform treatments and determine significant differences in their accuracy. For the hardware performance analysis, a FPGA synthesis methodology was adopted to quantify resource consumption and latency of the treatments. The results of the study showed that the discrete transforms direct treatment provide higher accuracy, and the highest resource consumption and latency. We observed in the accuracy analysis that as the resolution of the discrete transform computation incremented, the range magnitude of the treatments experimental normwise relative error incremented. But the range magnitude of the fast algorithms treatments incremented at a higher scale.