A discrete Fourier transform based on Simpson's rule.

Abstract

Fourier transforms are mathematical operations which play a vital role in the analysis of mathematical models for problems originating from a broad spectrum of elds. In this thesis, we formulate a discrete transform based on Simpson's quadrature for 4m + 2 quadrature nodes and analyse its various properties and provide detailed proofs thereof. In addition, we make applications to encryption and watermarking in the frequency domain.