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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.
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TL;DR: In this paper, a reversible eight-element discrete cosine transform coding system was proposed, which provides transform values near to transform values of the original 8-element DCT, by combining reversible transform quantization for a 4×4 matrix and conventional reversible quantization of 2×2 matrices.
Abstract: A reversible eight-element discrete cosine transform coding system which provides transform values near to transform values of the original eight-element discrete cosine transform. In a 4×4 matrix transform which appears when an eight-element discrete cosine transform is decomposed in accordance with a fast calculation method, transform coefficients (X1, X7, X3, X5) are separated into (X1, X7) and (X3, X5), which are quantized individually making use of the fact that, if (X1, X7) are determined, then values which can be taken by (X3, X5) are limited. (X1, X7) are quantized with step sizes k1, k7 by linear quantizers to obtain quantization values (Xq1, Xq7). Meanwhile, (X3, X5) are divided into global signals and local signals, and the global signals are quantized with step sizes L3, L5 by linear quantizers while quantization values of the local signals are determined using a table. The quantization values are added by adders to obtain quantization values (Xq3, Xq5) of (X3, X5). The reversible transform quantization for a 4×4 matrix and conventional reversible quantization of 2×2 matrices are combined to construct a reversible eight-element discrete cosine transform system.
24 citations
TL;DR: A recursive sparse matrix decomposition for a floating-point discrete cosine transform (DCT) matrix is presented and a split-radix DCT algorithm is proposed and a new integer DCT algorithms that requires only lifting steps and additions is developed.
Abstract: A recursive sparse matrix decomposition for a floating-point discrete cosine transform (DCT) matrix is presented. Based on this matrix decomposition approach, a split-radix DCT algorithm is proposed and a new integer DCT (IntDCT) algorithm that requires only lifting steps and additions is developed.
24 citations
TL;DR: Simulation indicates that the discrete cosine transform provides better initial values than discrete Fourier transform does, and it converges to a more accurate level by updating with spectrum-based slopes comparing to the slope updates from finite difference in classical method.
24 citations
TL;DR: An approximation to the discrete cosine transform (DCT) called the C -matrix transform (CMT) has been developed by Jones et al. as mentioned in this paper for N = 8 and its performance is compared with the DCT based on some standard criteria.
24 citations
TL;DR: In this article, a conjugate symmetry property which generalizes the well known property of the complex DFT for real data is presented for this situation, which is used to obtain a technique for computing the DFT of μ sequences with values in a ring S using a single DFT in an extension ring R of degree μ over S.
Abstract: Often, signals which lie in a ring S are convolved using a generalized discrete Fourier transform (DFT) over an extension ring R in order to allow longer sequence lengths. In this paper, a conjugate symmetry property which generalizes the well known property of the complex DFT for real data is presented for this situation. This property is used to obtain a technique for computing the DFT of μ sequences with values in a ring S using a single DFT in an extension ring R of degree μ over S. From this result, a method to compute the convolution of length μn S-sequences using a length n DFT in R is derived. Example of the application to the complex DFT and to a number theoretic transform are presented to illustrate the theory.
24 citations