Topic
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: It is interesting to note that the inverse transform is multiplication free, which enables fast inversion and eliminates the finite-word-length error that may be generated in performing the multiplications.
Abstract: In this correspondence, a discrete periodic Radon transform and its inversion are developed. The new discrete periodic Radon transform possesses many properties similar to the continuous Radon transform such as the Fourier slice theorem and the convolution property, etc. With the convolution property, a 2-D circular convolution can be decomposed into 1-D circular convolutions, hence improving the computational efficiency. Based on the proposed discrete periodic Radon transform, we further develop the inversion formula using the discrete Fourier slice theorem. It is interesting to note that the inverse transform is multiplication free. This important characteristic not only enables fast inversion but also eliminates the finite-word-length error that may be generated in performing the multiplications.
64 citations
TL;DR: Fast decimation-in-time algorithms for the various discrete cosine transforms and discrete sine transforms are systematically developed, based on a radix-2 factorization of the transformation matrix, and indicate these to be attractive alternatives to existing algorithms in terms of computational complexity and structural simplicity.
Abstract: Fast decimation-in-time (DIT) algorithms for the various discrete cosine transforms (DCT) and discrete sine transforms (DST) are systematically developed, based on a radix-2 factorization of the transformation matrix. The results indicate these to be attractive alternatives to existing algorithms in terms of computational complexity and structural simplicity.
64 citations
01 Jan 1979
TL;DR: This paper presents two methods for computing discrete Fourier transforms (DFT) by polynomial transforms and shows that these techniques are particularly well adapted to multidimensional DFTs as well as to some one-dimensional DFT's and yield algorithms that are, in many instances, more efficient than the fast Fourier transform (FFT) or the Winograd Fourier Transform (WFTA).
64 citations
TL;DR: In this article, the authors present general design formulae for optically implementing the two-dimensional fractional Fourier transform in two orthogonal dimensions and specify the two orders and the input, output scale parameters simultaneously.
64 citations
TL;DR: It is shown that such an algorithm is equivalent in computational complexity to the evaluation of a rectangular discrete Fourier transform, and a Chinese remainder theorem is derived for integer lattices.
Abstract: In this paper, the prime factor algorithm for the evaluation of a one-dimensional discrete Fourier transform is generalized to the evaluation of multidimensional discrete Fourier transforms defined on arbitrary periodic sampling lattices. It is shown that such an algorithm is equivalent in computational complexity to the evaluation of a rectangular discrete Fourier transform. As a sidelight to the derivation of the algorithm, a Chinese remainder theorem is derived for integer lattices.
64 citations