The discrete cosine transform (DCT) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. It is equivalent to a DFT of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), where in some variants the input and/or output data are shifted by half a sampl...

The discrete cosine transform (DCT) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. It is equivalent to a DFT of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), where in some variants the input and/or output data are shifted by half a sampl...

C06FKF Circular convolution or correlation of two real vectors, extra workspace for greater speed C06FPF Multiple one-dimensional real discrete Fourier transforms C06FQF Multiple one-dimensional Hermitian discrete Fourier transforms C06FRF Multiple one-dimensional complex discrete Fourier transforms C06FUF Two-dimensional complex discrete Fourier transform C06FXF Three-dimensional complex discr...

In signal processing applications, a key role is played by the Fourier transforms. The mathematical structure underlying Fourier analysis is the linear structure. In the present paper we propose and study a tool designed for nonlinear signal and image processing, that is novel Fourier-like transforms, based on a pair of pseudo-operations consisting of a uninorm and an absorbing norm. We analyse...

The 2-D Fourier transform has been generalized into the 2-D separable fractional Fourier transform (replaces 1-D Fourier transform by 1-D fractional Fourier transform for each variable) and the 2-D separable canonical transform (further replaces the fractional Fourier transform by canonical transform) in [3]. It also has been generalized into the 2-D unseparable fractional Fourier transform wit...

In [1], R. A. Kunze has presented a notion of generalized Fourier transform of functions on locally compact abelian groups. The point of this paper is to extend this idea in the direction of distribution theory and to present some initial results on this generalized Fourier transform of distributions. In a later paper we hope to investigate in detail the domain, range, and kernel of this transf...

Fourier Transforms have been available for PureData for a long time. However they have never been applied to pixels, not ounting the possibility that someone onverted an image to sound in order to use [ t~℄ on it, whi h is fastidious and is still just a one-dimensional transform. This paper exposes the possibilities of using Fourier Transforms on whole images and on sequen es of them that enabl...

We propose a definition for quantum Fourier transforms in settings where the algebraic structure is that of a finite field, and show that they can be performed efficiently by a quantum computer. Using these finite field quantum Fourier transforms, we obtain the strongest separation between quantum and classical query complexity known to date—specifically, we define a problem that requires Ω(2) ...

It is suggested that, given the magnitude of Fourier transforms sampled at the Bragg density, the phase problem is underdetermined by a factor of 2 for 1D, 2D, and 3D objects. It is therefore unnecessary to oversample the magnitude of Fourier transforms by 23 in each dimension (i.e., oversampling by 43 for 2D and 83 for 3D) in retrieving the phase of 2D and 3D objects. Our computer phasing expe...

Fourier methods used in 2and 3-dimensional image reconstruction can be used also in reconstructability analysis (RA). These methods maximize a variance-type measure instead of information-theoretic uncertainty, but the two measures are roughly colinear and the Fourier approach yields results close to those of standard RA. The Fourier method, however, does not require iterative calculations for ...