FAST DHT ALGORITHMS FOR COMPOSITE SEQUENCE LENGTHS

1998 ◽  
Vol 08 (03) ◽  
pp. 421-434
Author(s):  
GUOAN BI ◽  
YANQIU CHEN
Keyword(s):  
Fourier Transforms ◽  
Fast Algorithms ◽  
Sequence Length ◽  
Discrete Fourier Transforms ◽  
One Dimensional ◽  
Discrete Hartley Transform ◽  
Hartley Transform ◽  
Computational Structure ◽  
The One

This paper presents fast algorithms for the computation of discrete Hartley transform (DHT). When the sequence length N = p*q, where p and q are integers and relatively prime, the one dimensional DHT can be decomposed into p length-q DHT's and q length-p discrete Fourier transforms (DFT). Compared to other reported algorithms, the proposed one has a regular computational structure, provides flexibility for composite sequence lengths and achieves substantial savings on the required number of operations.

The shift lattice: an interpretation of some infinitely adaptive structures

1993 ◽  
Vol 440 (1908) ◽  
pp. 23-36 ◽  
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Periodic Systems ◽  
Adaptive Structures ◽  
One Dimensional ◽  
Modulated Structures ◽  
Simple Generalization ◽  
The One

The structures of various ordered, but non-periodic, systems have been investigated and exhibit features which can be directly described by means of a construction which the authors call the shift lattice , which is a simple generalization of the concept of the lattice. This paper is devoted to a description of the properties of the one-dimensional shift lattice and its Fourier transform. Its applications to the phases related to L–Ta 2 O 5 and some Bi 2 TeO 5 -related systems are outlined and its relation to the theory of modulated structures and their Fourier transforms is briefly discussed.

Genetic-Algorithm-Based Optimization of Fragile Watermarking in Discrete Hartley Transform Domain

2016 ◽  
pp. 103-127
Author(s):  
Sudipta Kr Ghosal ◽  
Jyotsna Kumar Mandal
Keyword(s):  
Genetic Algorithm ◽  
Color Images ◽  
Fragile Watermarking ◽  
Transform Domain ◽  
One Dimensional ◽  
Discrete Hartley Transform ◽  
Hartley Transform ◽  
Message Digest ◽  
Simulation Results ◽  
Watermarking Scheme

In this chapter, a fragile watermarking scheme based on One-Dimensional Discrete Hartley Transform (1D-DHT) has been proposed to verify the authenticity of color images. One-Dimensional Discrete Hartley Transform (1D-DHT) converts each 1 x 2 sub-matrix of pixel components into transform domain. Watermark (along with a message digest MD) bits are embedded into the transformed components in varying proportion. To minimize the quality distortion, genetic algorithm (GA) based optimization is applied which yields the optimized component corresponding to each embedded component. Applying One-Dimensional Inverse Discrete Hartley Transform (1D-IDHT) on 1 x 2 sub-matrices of embedded components re-generates the pixel components in spatial domain. The reverse approach is followed by the recipient to retrieve back the watermark (along with the message digest MD) which in turn is compared against the re-computed Message Digest (MD') for authentication. Simulation results demonstrate that the proposed technique offers variable payload and less distortion as compared to existing schemes.

FAST ALGORITHMS FOR GENERALIZED DISCRETE HARTLEY TRANSFORM

2000 ◽  
Vol 10 (01n02) ◽  
pp. 77-83 ◽  
Author(s):  
GUOAN BI ◽  
SHOUTIAN LIAN
Keyword(s):  
Substantial Reduction ◽  
Fast Algorithms ◽  
Mapping Method ◽  
Discrete Hartley Transform ◽  
Type Iii ◽  
Hartley Transform ◽  
Simple Index ◽  
Index Mapping ◽  
Factor Decomposition ◽  
P Type

Based on the prime factor decomposition, this paper presents fast algorithms for type-III generalized discrete Hartley transform (GDHT). When N = p*q, where p and q are mutually prime, the length-N GDHT can be decomposed into p length-q type-III GDHT and q length-p type-III discrete cosine transform (DCT). The proposed algorithms achieve a substantial reduction of the number of additions and multiplications and possess a regular computational structure. In particular, a simple index mapping method is proposed to minimize the overall implementation complexity and cost.

X-ray diffraction of helices with arbitrary periodic ligand binding

1999 ◽  
Vol 55 (12) ◽  
pp. 2022-2027 ◽  
Author(s):  
Jin Gu ◽  
Leepo C. Yu
Keyword(s):  
Ligand Binding ◽  
Fourier Transforms ◽  
Muscle Actin ◽  
X Ray Diffraction ◽  
Helical Structures ◽  
One Dimensional ◽  
X Ray ◽  
Classical Formalism ◽  
Diffraction Patterns ◽  
The One

The classical formalism for studying diffraction from helical structures extended to include ligand binding is presented. The diffraction from such a binding pattern is the convolution of the Fourier transforms of the helix and the one-dimensional binding distribution. It is shown in the present analysis that it is not necessary to assume that the binding distribution is strictly periodic, as long as its Fourier transform can be determined. Analysis of the convolution gives a general expression for the diffracted intensities and the selection rule for the layer-lines. It shows two groups of layer-lines: one group is the familiar layer-line set from the original helix, while the other group shows reciprocal spacings shifted by 1/a from the original helix layer-lines, where a is the average repeat of the binding distribution. This group of layer-lines is contributed by the ligand only. By way of examples, calculated diffraction patterns from muscle actin filaments with bound myosin heads in three different binding patterns are presented. This approach provides a method for determining the ligand-binding distribution along helices by an analysis of their X-ray diffraction patterns.

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