The Gale transform is an involution on sets of points in a projective space. It plays a crucial role in several different subjects, such as algebraic geometry, optimization, coding theory, and so on. We give a brief survey—from a finite geometry point of view—on the algebraic and geometrical implications of the Gale transform with emphasis on its applications to coding theory, and describe some...

Powerline interference always disturbs recordings of biomedical signals. Numerous methods have been developed to reduce powerline interference. However, most of these techniques not only reduce the interference but also attenuate the 60 Hz power of the biomedical signals themselves. In the present study, we applied the S-transform, which provides an absolute phase of each frequency in a multi-r...

We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to S nor to S. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms fr...

DES can be regarded as a nonlinear feedback shift register (NLFSR) with input. From this point of view, the tools for pseudo-random sequence analysis are applied to the S-boxes in DES. The properties of the S-boxes of DES under Fourier transform, Hadamard transform, extended Hadamard transform and Avalanche transform are investigated. Two important results about the S-boxes of DES are found. Th...

In this paper, we propose a novel method for facial feature extraction using the directional multiresolution decomposition offered by the complex wavelet transform. The dual-tree implementation of complex wavelet transform offered by Selesnick is used (DT-DWT(S)) [I.W., Selesnick, R.G. Baraniuk, N.C. Kingsbury, The dual-tree complex wavelet transform, IEEE Signal Processing Magazine, 6, s.l., I...

The accurate classification of power quality disturbance (PQD) signals is great significance for the establishment a real-time monitoring system modern grids, ensuring safe and stable operation electricity safety users. Traditional signal methods are susceptible to noise interference, feature selection, etc. In order further improve accuracy methods, this paper proposes method based on S-transf...

Introducing a suitable variational formulation for the local error of scattered data interpolation by radial basis functions (r), the error can be bounded by a term depending on the Fourier transform of the interpolated function f and a certain \Kriging function", which allows a formulation as an integral involving the Fourier transform of. The explicit construction of locally well{behaving adm...