Singh, Pravin.Singh, Virath Sewnath.Sibandze, Dan Behlule.2015-01-052015-01-0520132013http://hdl.handle.net/10413/11809M. Sc. University of KwaZulu-Natal, Durban 2013.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.en-ZAFourier analysis.Fourier transformations.Eigenvalues.Matrices.Theses--Applied mathematics.Thesis