Hilbert and Hadamard transforms by generalized Chebyshev expansion

Generalized multidimensional Hilbert transforms in Clifford analysis

During the last fifty years, Clifford analysis has gradually developed to a comprehensive theory offering a direct, elegant, and powerful generalization to higher dimension of the theory of holomorphic functions in the complex plane. In its most simple but still useful setting, flat m-dimensional Euclidean space, Clifford analysis focusses on the so-called monogenic functions, that is, null sol...

2D Image Analysis by Generalized Hilbert Transforms in Conformal Space

This work presents a novel rotational invariant quadrature filter approach called the conformal monogenic signal for analyzing i(ntrinsic)1D and i2D local features of any curved 2D signal such as lines, edges, corners and junctions without the use of steering. The conformal monogenic signal contains the monogenic signal as a special case for i1D signals and combines monogenic scale space, phase...

Multidimensional Fast Gauss Transforms by Chebyshev Expansions

A new version of the fast Gauss transform (FGT) is introduced which is based on a truncated Chebyshev series expansion of the Gaussian. Unlike the traditional fast algorithms, the scheme does not subdivide sources and evaluation points into multiple clusters. Instead, the whole problem geometry is treated as a single cluster. Estimates for the error as a function of the dimension d and the expa...

Fast Pseudo-Hadamard Transforms

We prove that the fast pseudo-Hadamard transform (FPHT) over a finite field has a bounded branch number. We shall demonstrate that the transform has an efficient implementation for various platforms compared to an equal dimension MDS code. We prove that when using a CS-Cipher[3] like construction the weight of any 2R trail is bounded for the case of an 8 × 8 transform. We show that the FPHT can...

Chebyshev Centers and Approximation in Pre-Hilbert C*-Modules