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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: A linear systolic array for the discrete cosine transform, discrete sine transform and their inverses is developed, which has the advantages of pipelinability, regularity, locality, and scalability, making it quite suitable for VLSI signal processing.
Abstract: A linear systolic array for the discrete cosine transform, discrete sine transform, and their inverses is developed. It generates the transform kernel values recursively. Compared to the scheme with the transform kernel values prestored in memory either inside or outside each processing element, the clock period is shortened by a memory access time. In addition, the array pays no cost for prestorage. The systolic array has the advantages of pipelinability, regularity, locality, and scalability, making it quite suitable for VLSI signal processing. >
77 citations
TL;DR: These new structured recursive algorithms are able to decompose the DCT and the DST into two balanced lower-order subproblems in comparison to previous research works, and require fewer hardware components than other recursive algorithms.
Abstract: The discrete cosine transform (DCT) and the discrete sine transform (DST) have found wide applications in speech and image processing, as well as telecommunication signal processing for the purpose of data compression, feature extraction, image reconstruction, and filtering. In this paper, we present new recursive algorithms for the DCT and the DST. The proposed method is based on certain recursive properties of the DCT coefficient matrix, and can be generalized to design recursive algorithms for the 2-D DCT and the 2-D DST. These new structured recursive algorithms are able to decompose the DCT and the DST into two balanced lower-order subproblems in comparison to previous research works. Therefore, when converting our algorithms into hardware implementations, we require fewer hardware components than other recursive algorithms. Finally, we propose two parallel algorithms for accelerating the computation. >
77 citations
TL;DR: A space-vector discrete-time Fourier transform is proposed for fast and precise detection of the fundamental-frequency and harmonic positive- and negative-sequence vector components of three-phase input signals.
Abstract: In this paper, a space-vector discrete-time Fourier transform is proposed for fast and precise detection of the fundamental-frequency and harmonic positive- and negative-sequence vector components of three-phase input signals. The discrete Fourier transform is applied to the three-phase signals represented by Clarke's αβ vector. It is shown that the complex numbers output from the Fourier transform are the instantaneous values of the positive- and negative-sequence harmonic component vectors of the input three-phase signals. The method allows the computation of any desired positive- or negative-sequence fundamental-frequency or harmonic vector component of the input signal. A recursive algorithm for low-effort online implementation is also presented. The detection performance for variable-frequency and interharmonic input signals is discussed. The proposed and other usual method performances are compared through simulations and experiments.
77 citations
TL;DR: This correspondence shows that the amount of work can be cut to doing two single length FFT's, which is equivalent to doing one double length fast Fourier transform.
Abstract: Ahmed has shown that a discrete cosine transform can be implemented by doing one double length fast Fourier transform (FFT). In this correspondence, we show that the amount of work can be cut to doing two single length FFT's.
77 citations
TL;DR: A notion of 2D discrete Radon transforms for2D discrete images, which is based on summation along lines of absolute slope less than 1, is defined, and is shown to be geometrically faithful: the summation avoids wrap-around effects.
Abstract: Although naturally at the heart of many fundamental physical computations, and potentially useful in many important image processing tasks, the Radon transform lacks a coherent discrete definition for two-dimensional (2D) discrete images which is algebraically exact, invertible, and rapidly computable. We define a notion of 2D discrete Radon transforms for 2D discrete images, which is based on summation along lines of absolute slope less than 1. Values at nongrid locations are defined using trigonometric interpolation on a zero-padded grid. Our definition is shown to be geometrically faithful: the summation avoids wrap-around effects. Our proposal uses a special collection of lines in $\mathbb{R}^{2}$ for which the transform is rapidly computable and invertible. We describe a fast algorithm using $O(N\log{N})$ operations, where $N =n^{2}$ is the number of pixels in the image. The fast algorithm exploits a discrete projection-slice theorem, which associates the discrete Radon transform with the pseudopolar Fourier transform [A. Averbuch et al., SIAM J. Sci. Comput., 30 (2008), pp. 764-784]. Our definition for discrete images converges to a natural continuous counterpart with increasing refinement.
77 citations