| This thesis presents a theoretical and experimental study of discrete Fourier transform based interpolation and approximation problems. Upon the observation that the Gibbs phenomenon occurs at the vicinity of the discontinuity point of a function approximated by a Fourier series, a linear transform is introduced in this work that eliminates the discontinuity at the periodical boundary when a discrete signal with finite duration is expanded periodically due to the property of discrete Fourier transform. Hence the accuracy of the interpolation or approximation is greatly improved. This technique is also extended to two-dimensional image zooming in this thesis and much better visual results are observed. Also, a C-code program implementing the image zooming algorithm is provided in this thesis. |
