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.

An Exact and Fast Computation of Discrete Fourier Transform for Polar and Spherical Grid

Abstract: Numerous applied problems of two-dimensional (2-D) and 3-D imaging are formulated in continuous domain. They place great emphasis on obtaining and manipulating the Fourier transform in polar and spherical coordinates. However, the translation of continuum ideas with the discrete sampled data on a Cartesian grid is problematic. There exists no exact and fast solution to the problem of obtaining discrete Fourier transform for polar and spherical grids in the literature. In this paper, we develop exact algorithms to the above problem for 2-D and 3-D, which involve only 1-D equispaced fast Fourier transform with no interpolation or approximation at any stage. The result of the proposed approach leads to a fast solution with very high accuracy. We describe the computational procedure to obtain the solution in both 2-D and 3-D, which includes fast forward and inverse transforms. We find the nested multilevel matrix structure of the inverse process, and we propose a hybrid grid and use a preconditioned conjugate gradient method that exhibits a drastic improvement in the condition number.

A multiplication-free digital architecture for 16×16 2-D DCT/DST transform for HEVC

Abstract: The discrete cosine transform (DCT) is widely employed in image and video coding applications due to its high energy compaction. In addition to 4×4 and 8×8 transforms utilized in earlier video coding standards, the proposed HEVC standard suggests the use of larger transform sizes including 16 × 16 and 32×32 transforms in order to obtain higher coding gains. Further, it also proposes the use of non-square transform sizes as well as the use of the discrete sine transform (DST) in certain intra-prediction modes. The decision on the type of transform used in a given prediction scenario is dynamically made, to obtain required compression rates. This motivated the proposed digital VLSI architecture for a multitransform engine capable of computing 16×16 approximate 2-D DCT/DST transform, with null multiplicative complexity. The relationship between DCT-II and DST-II is employed to compute both transforms using the same digital core, leading to reductions in both area and power. Closed-form relationship between the 16×16 transform and arbitrary smaller sized transform is presented, enabling the usability of this architecture to compute transforms of size 4 · 2P × 4 · 2q where 0 ≤ p, q ≤ 2.

Fast construction of Fejér and Clenshaw-Curtis rules for general weight functions

Abstract: The main purpose of this paper is to compute the weights of Clenshaw-Curtis and Fejer type quadrature rules via DCT and DST, for general weight functions w. The approach is different from that used by Waldvogel (2006) in [10], where the author considered the computation of these sets only for the Legendre weight w=1 using DFT arguments.