Hartley transform

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

Efficient Fast Fourier Transform Programs for Arbitary Factors with One Step Loop Unscrambling

Abstract: This correspondence develops efficient fast Fourier transform (FFT) programs to transform arrays of dimension N, where N can be written as a power of two possibly multiplied by arbitrary factors. Two programs were developed which use radix-2 and radix-4 transformations for the binary factors. These programs call another subprogram to transform with respect to the arbitrary factors, if any. Since the sequential transformation is well known, the emphasis is on developing an efficient unscrambling procedure to follow the transformation.

On unified architectures for synthesizing and implementation of fast parametric transforms

Abstract: In this paper a methodology to design VLSI architectures for parametric transform families is proposed. A parametric transform family consists of discrete orthogonal transforms such that they all may be computed with a fast algorithm of similar structure where parameters defining the transform within the family are used. In our previous work, an algorithm to synthesize transforms with predefined basis functions was introduced and efficiently applied to image compression. The methodology proposed in this paper allows of designing VLSI architectures that may not only switch from one transform of a family to another by setting parameters, but also to actually set these parameters so that the matrix of the resulting transform has predefined basis functions

Low complexity partial parallel architectures for fourier transform and inverse fourier transform over subfields of a finite field

Abstract: Low complexity partial parallel architectures for performing a Fourier transform and an inverse Fourier transform over subfields of a finite field are described. For example, circuits to perform the Fourier transforms and the inverse Fourier transform as described herein may have architectures that have simplified multipliers and/or computational units as compared to traditional Fourier transform circuits and traditional inverse Fourier transform circuits that have partial parallel designs. In a particular embodiment, a method includes, in a data storage device including a controller and a non-volatile memory, the controller includes an inverse Fourier transform circuit having a first number of inputs coupled to multipliers, receiving elements of an input vector and providing the elements to the multipliers. The multipliers are configured to perform calculations associated with an inverse Fourier transform operation. The first number is less than a number of inverse Fourier transform results corresponding to the inverse Fourier transform operation.

A Reciprocal-Orthogonal Parametric Transform and Its Fast Algorithm

Abstract: In this letter, a reciprocal-orthogonal parametric transform and an efficient algorithm for its simple construction and fast computation are proposed. The algorithm is developed by introducing a recursive approach to decompose the transform matrix into a product of sparse matrices using the Kronecker product. It is shown that the structure of the resulting algorithm is very similar to that of the well-known Walsh-Hadamard transform, except for the multipliers introduced by the independent parameters. The transform has a large number of independent parameters that can be chosen arbitrarily from the complex plane. Thus, many interesting special cases can easily be obtained from the proposed transform. Moreover, we carry out a number of experiments to show that its independent parameters can successfully be used as an additional secret key for image encryption.