Date of Award

Fall 2003

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Electrical & Computer Engineering

Program/Concentration

Computer Engineering

Committee Director

Vijayan K. Asari

Committee Member

Linda L. Vahala

Committee Member

Min Song

Call Number for Print

Special Collections LD4331.E55 R385 2003

Abstract

CORDIC (Coordinate Rotation Digital Computer) is an iterative algorithm to compute values of trigonometric, logarithmic and transcendental functions by performing vector rotations, which can be implemented with only shift and add operations in a digital system. CORDIC algorithms are extensively used in the areas of digital signal processing, digital image processing and artificial neural networks. A new technique, named unidirectional CORDIC, for efficient computation of trigonometric and hyperbolic functions is presented in this thesis. In the conventional CORDIC algorithm, the vector rotations are performed in both clockwise and counterclockwise directions, but in the unidirectional CORDIC the vectors are rotated only in one direction. This leads to a reduction of the number of vector rotations required to compute a value and hence unidirectional CORDIC approach contributes significant improvement in speed and power savings in digital systems.

A novel technique of pre-computation of the rotation bits from a given angle is presented in this thesis. This would help increase the performance of the CORDIC architecture in both speed and power consumption. The pre-computed rotation bits are predominantly useful for the implementation of unidirectional Flat-CORDIC, which is a parallel form of CORDIC algorithm to compute the values in one clock cycle. The unidirectional CORDIC module along with the circuitry for pre-computation of rotation bits is implemented in a FPGA (Fie1d Programmable Gate Array) environment using Alters Quartos II design tool. Hardware simulation results of the unidirectional CORDIC algorithm in the computations of trigonometric and hyperbolic functions with 24 bit input angle show accurate results with error less than 10-8.

A technique for the training of multiple-valued neural networks based on backpropagation learning rule employing a multilevel threshold function is also presented in this thesis as an application of unidirectional CORDIC algorithm. The multilevel threshold function is developed as a sum of shifted and scaled hyperbolic tangent functions created by the unidirectional CORDIC technique. The optimum threshold width of the multilevel function and the range of the learning rate parameter to be chosen for convergence are derived. Trials performed on a benchmark problem demonstrate the convergence of the network within the specified range of parameters. An important advantage of the multiple-valued neural network is that it can be implemented in VLSI with reduced number of neurons and synaptic weights.

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DOI

10.25777/n9px-6a20

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