Computing the Fourier transform and its inverse is important in many applications of mathematics, such as frequency analysis, signal modulation, and filtering. Two methods will be derived for numerically computing the inverse Fourier transforms, and they will be compared to the standard inverse discrete Fourier transform (IDFT) method. The first computes the inverse Fourier transform through di...

We study a generalization of the Fourier-Mukai transform for smooth projective varieties. We find conditions under which the transform satisfies an inversion theorem. This is done by considering a series of four conditions on such transforms which increasingly constrain them. We show that a necessary condition for the existence of such transforms is that the first Chern classes must vanish and ...

We study a generalization of the Fourier-Mukai transform for smooth projective varieties. We nd conditions under which the transform satisses an inversion theorem. This is done by considering a series of four conditions on such transforms which increasingly constrain them. We show that a necessary condition for the existence of such transforms is that the rst Chern classes must vanish and the d...

An algorithm is presented allowing the construction of fast Fourier transforms for any solvable group on a classical computer. The special structure of the recursion formula being the core of this algorithm makes it a good starting point to obtain systematically fast Fourier transforms for solvable groups on a quantum computer. The inherent structure of the Hilbert space imposed by the qubit ar...

In this paper, an approach to lossy image compression using 1-D wavelet transforms is proposed. The analyzed image is divided in little subimages and each one is decomposed in vectors following a fractal Hilbert curve. A Wavelet Transform is thus applied to each vector and high frequency components are suppressed. The Huffman coding algorithm is then applied in order to reduce image weight. The...