Let G be a locally compact group. We show that its Fourier algebra A(G) is amenable if and only if G has an abelian subgroup of finite index, and that its Fourier– Stieltjes algebra B(G) is amenable if and only if G has a compact, abelian subgroup of finite index.

Edge detection plays an important role in identifying regions of interest in an underlying signal or image. In some applications, such as magnetic resonance imaging (MRI) or synthetic aperture radar (SAR), data are sampled in the Fourier domain. Many algorithms have been developed to efficiently extract edges of images when uniform Fourier data are acquired. However, in cases where the data are...

Local keypoint detection and description have been widely employed in a large number of computer vision applications, such as image registration, object recognition and robot localisation. Since currently available local keypoint descriptors are based on the uses of statistical analysis in spatial domain, a local keypoint descriptor, namely Radial Fourier Analysis (RFA) keypoint descriptor, is ...

and the inverse Fourier transform is f (x) = 1 2π ∫ ∞ −∞ F(ω)e dω Recall that i = √−1 and eiθ = cos θ+ i sin θ. Think of it as a transformation into a different set of basis functions. The Fourier transform uses complex exponentials (sinusoids) of various frequencies as its basis functions. (Other transforms, such as Z, Laplace, Cosine, Wavelet, and Hartley, use different basis functions). A Fo...

A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT's in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from -1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT...

Direct-phi perception elicited by a reverse-phi (i.e. reversed-polarity) stimulus may well be accounted for, if the front-end filters of a classical Reichardt unit are full-wave rectifiers. It is shown that reverse-phi perception is progressively replaced by direct-phi perception when either the spatial or the temporal modulation of the reversed-polarity stimuli are decreased. Reverse-phi perce...