Discrete sine transform

About: Discrete sine transform is a research topic. Over the lifetime, 3269 publications have been published within this topic receiving 73181 citations.

Fast computation of multidimensional discrete fourier transforms

Abstract: An algorithm is presented, for the computation of multidimensional Fourier and Fourier-like discrete transforms, which offers substantial savings in the number of multiplications over the conventional fast Fourier transform method Implementation of this algorithm, and the use of it to compute discrete Fourier transforms of real sequences, are also described

Seismic data compression

Abstract: An investigation of low-rate seismic data compression using transform techniques is presented. This study concentrates on discrete orthogonal transforms such as the discrete Fourier transform (DFT), the discrete cosine transform (DCT), the Walsh-Hadamard transform (WHT), and the Karhunen-Loeve transform (KLT). Uniform and subband transform coding schemes are implemented, and comparative results are given for data rates ranging from 150 to 550 b/s. Results are also compared with existing linear prediction techniques. >

Two VLSI Structures for the Discrete Fourier Transform

Abstract: Two VLSI structures for the computation of the discrete Fourier transform are presented. The first structure is a pipeline working concurrently on different transforms. It is shown that it matches, within a constant factor, the theoretical lower bounds for area versus data rate. The second structure is a simple modification of the first one; it works on a single transform at a time, and it matches within a constant factor the theoretical area-time lower bounds.

Fractionalisation of an odd time odd frequency DFT matrix based on the eigenvectors of a novel nearly tridiagonal commuting matrix

Abstract: The discrete equivalent of Hermite-Gaussian functions (HGFs) plays a critical role in the definition of a discrete fractional Fourier transform (DFRFT). The discrete equivalents are typically calculated through the eigendecomposition of a commutator matrix. In this study, the authors mainly focus on the fractionalisation of an odd time odd frequency discrete Fourier transform (O-ODFT) matrix. First, the authors propose a novel nearly tridiagonal matrix, which commutes with the O-ODFT matrix. It does not have multiple eigenvalues. The authors can determine a unique orthonormal eigenvector set based on block diagonalisation of a new commuting matrix. The eigenvectors of the new nearly tridiagonal matrix are shown to be O-ODFT eigenvectors, which are similar to the continuous HGFs. Then, the result of the eigendecomposition of the transform matrix is used in order to define the fractionalisation of O-ODFT (O-ODFRFT). The definition is exactly unitary, index additive and reduces to the O-ODFT for unit order. Finally, numerical examples are illustrated to demonstrate that the proposed O-ODFRFT is approximated to the continuous fractional Fourier transform.

Robustness analysis of image watermarking based on discrete fractional random transform

Abstract: The robustness of a watermarking scheme based on the discrete fractional random transform has been investigated and demonstrated to be superior to those based on the discrete cosine transform, discrete fractional Fourier transform, and discrete Fourier transform The spectrum distribution of the discrete fractional random transform is random and uniform, which guarantees good robustness In addition, the discrete fractional random transform itself can serve as a secret key, and can provide high capacity while ensuring robustness in image hiding Moreover, the feature of real output of the discrete fractional random transform with a half periodicity in its eigenvalues can save storage space of image data and is convenient for storage Numerical simulations have confirmed our analysis and demonstrated the superiority of the discrete fractional random transform