We study the restriction of the Fourier transform to quadratic surfaces in vector spaces over finite fields. In two dimensions, we obtain the sharp result by considering the sums of arbitrary two elements in the subset of quadratic surfaces on two dimensional vector spaces over finite fields. For higher dimensions, we estimate the decay of the Fourier transform of the characteristic functions o...

Linear spectral transform techniques such as the discrete Fourier transform and wavelet analysis over real and complex fields have been routinely applied in the literature (Burrus et al. (1998); Strang & Nuygen (1996)). Furthermore, extensions of these techniques over finite fields (Blahut & Burrus (1991); Caire et al. (1993)) have led to applications in the areas of information theory and erro...

Finite Fourier integrals of functions possessing jumps in value, in the first or in the second derivative, are shown to be evaluated more efficiently, and more accurately, using a continuous Fourier transform (CFT) method than the discrete transform method used by the fast Fourier transform (FFT) algorithm. A ß-spline fit is made to the input function, and the Fourier transform of the set of B-...

Post-processing in computational fluid dynamics as well as processing of fluid flow measurements needs robust methods that can deal with scalar as well as vector fields. While image processing of scalar data is a well-established discipline, there is a lack of similar methods for vector data. This paper surveys a particular approach defining convolution operators on vector fields using geometri...

The paper studies the vector space of set functions on a finite set X, which can be alternatively seen as pseudo-Boolean functions, and including as a special cases games. We present several bases (unanimity games, Walsh and parity functions) and make an emphasis on the Fourier transform. Then we establish the basic duality between bases and invertible linear transform (e.g., the Möbius transfo...