Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.

Matters Computational: Ideas, Algorithms, Source Code

Abstract: Low level algorithms.- Bit wizardry.- Permutations and their operations.- Sorting and searching.- Data structures.- Combinatorial generation.- Conventions and considerations.- Combinations.- Compositions.- Subsets.- Mixed radix numbers.- Permutations.- Multisets.- Gray codes for string with restrictions.- Parenthesis strings.- Integer partitions.- Set partitions.- Necklaces and Lyndon words.- Hadamard and conference matrices.- Searching paths in directed graphs.- Fast transforms.- The Fourier transform.- Convolution, correlation, and more FFT algorithms.- The Walsh transform and its relatives.- The Haar transform.- The Hartley transform.- Number theoretic transforms (NTTs).- Fast wavelet transforms.- Fast arithmetic.- Fast multiplication and exponentiation.- Root extraction.- Iterations for the inversion of a function.- The AGM, elliptic integrals, and algorithms for computing.- Logarithm and exponential function.- Computing the elementary functions with limited resources.- Numerical evaluation of power series.- Cyclotomic polynomials, product forms, and continued fractions.- Synthetic Iterations.-. Algorithms for finite fields.- Modular arithmetic and some number theory.- Binary polynomials.- Shift registers.- Binary finite fields.- The electronic version of the book.- Machine used for benchmarking.- The GP language.- Bibliography.- Index.

Digital filtering using pseudo fermat number transforms

Abstract: In this paper pseudo Fermat number transforms (FNT's) are discussed. These transforms are defined in a ring of integers modulo an integer submultiple of a pseudo Fermat number, and can be computed without multiplications while allowing a great flexibility in word length selection. Complex pseudo FNT's are then introduced and are shown to relieve some of the length limitations of conventional Fermat number transforms (FNT's). These transforms, which under certain conditions can be computed via fast transform algorithms allow the implementation of digital filters with better efficiency and accuracy than the fast Fourier transform (FFT).

Analytic properties of the Hartley transform and their implications

Abstract: The Hartley transform is an integral transform closely related to the Fourier transform. It has some advantages over the Fourier transform in the analysis of real signals as it avoids the use of complex arithmetic. However, the Hartley transform has other applications in signal and image reconstruction related to traditional phase retrieval problems. These can he understood by examining the analytic properties of the Hartley transform in the complex plane. In this paper, the analytic continuation of the Hartley transform into the complex plane is derived and its properties discussed. It is shown that for signals or images of finite extent, the Hartley transform is analytic in the entire finite complex plane, and this is used to derive properties of its complex zeros. Hilbert transform-type relationships for the Hartley transform, related to causal and analytic-signals, are also derived. The analytic properties derived are used to study the problem of image reconstruction from the Hartley transform intensity. Uniqueness and reconstruction algorithms for one- and two-dimensional problems are discussed, and examples are presented. Generation of image moments from the Hartley transform intensity is also described. >