Hartley transform

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

On the diagonalization of the discrete Fourier transform

Abstract: The discrete Fourier transform (DFT) is an important operator which acts on the Hilbert space of complex valued functions on the ring Z/NZ. In the case where N=p is an odd prime number, we exhibit a canonical basis of eigenvectors for the DFT. The transition matrix from the standard basis to the canonical basis defines a novel transform which we call the discrete oscillator transform (DOT for short). Finally, we describe a fast algorithm for computing the discrete oscillator transform in certain cases.

Fourier transform based techniques in efficient retrieval of similar time sequences

Abstract: Fourier-Transform Based Techniques in Efficient Retrieval of Similar Tirne Sequences Davood Rafiei Doctor of Philosophy Graduate Department of Computer Science University of Toronto 1999 The idea of posing queries in terms of similarity of objects, rather than equality or inequality, is of growing importance in new database applications, such as data mining or data warehousing. In this dissertation, the notion of similarity is defined in terms of a distance function and a set of linear transformations. This turns out to be a proper notion of similarity for time series data since it can eliminate seasonal effects and shortterm fluctuations before aligning them. The focus of this dissertation is on efficiently processing s i rn i l~ i ty queries on time series data. The dissertation first describes an important property of real-valued time sequences in the frequency domain, i.e. symmetry, and presents an algorithm that uses this property to improve the performance of a multidimensional index built on a sequence data set by more than a factor of two. This improvement is confirmed both analytically and

Linear and nonlinear generalized Fourier transforms

Abstract: This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.

Image encryption using block based transformation with fractional Fourier transform

Abstract: In order to transmit image data in open network, a novel image encryption algorithm based on fractional Fourier transform and block-based transformation is proposed in this paper. The image encryption process includes two steps: the original image was divided into blocks, which were rearranged into a transformed image using a transformation algorithm, and then the transformed image was encrypted using the fractional Fourier transform (FRFT) algorithm. The security of the proposed algorithm depends on the transformation algorithm, sensitivity to the randomness of phase mask and the orders of FRFT. Theoretical analysis and experimental results demonstrate that the algorithm is favorable.

Method and apparatus for fast image compression

Abstract: An image compression scheme uses a reversible transform, such as the Discrete Hartley Transform, to efficiently compress and expand image data for storage and retrieval of images in a digital format. The image data is divided into one or more image sets, each image set representing a rectangular array of pixel data from the image. Each image set is transformed using a reversible transform, such as the Hartley transform, into a set of coefficients which are then quantized and encoded using an entropy coder. The resultant coded data sets for each of the compressed image sets are then stored for subsequent expansion. Expansion of the stored data back into the image is essentially the reverse of the compression scheme.