A Fast Recursive Algorithm For Computing The Discrete Cosine Transform

Hou, H. S.

doi:10.1117/12.976201

Cited by 75 publications

(87 citation statements)

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“…Recursive implementation of DCTs [22], with parallel processing blocks, can also be used, especially for large filters to reduce computations by a large amount. The stability of the HBNLMS algorithm vis-à-vis rounding off errors can be studied equivalently by studying the stability of the various DCT algorithms in comparison with the stability of the real FFT algorithms used in FBNLMS.…”

Section: Discussionmentioning

confidence: 99%

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An analysis of real-Fourier domain-based adaptive algorithms implemented with the Hartley transform using cosine-sine symmetries

Raghavan

Prabhu

Sommen

2005

IEEE Trans. Signal Process.

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Section: Discussionmentioning

confidence: 99%

“…Then, the 2N-point Hartley transform of is (27) Since the DCT-II of x(n) is implemented recursively using an even and an odd breakup [21], [22], the DCT-II of (and thus the DST-II and the DST-I) can be easily computed. The block diagram of a DST-I transformer is shown in Fig.…”

Section: Implementation Of the Hbnlmsmentioning

confidence: 99%

An analysis of real-Fourier domain-based adaptive algorithms implemented with the Hartley transform using cosine-sine symmetries

Raghavan

Prabhu

Sommen

2005

IEEE Trans. Signal Process.

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“…Thus, the proposed systematic decomposition is based on the Jacket and Hadamard matrices. In [17], the author proposed a recursive decimation-in-frequency algorithm, where the same decomposition specified in (10) was used. However, due to using a different permutation matrix, a different recursive form was obtained.…”

Section: Proofmentioning

confidence: 99%

“…Further applying (17) to the Kronecker product ½I 2 Y N=2 , the following general recursive form for the DST-II matrix can be obtained as …”

Section: Diagonal Block-wise Inverse Sparse Matrix Decomposition the mentioning

confidence: 99%

A fast hybrid Jacket–Hadamard matrix based diagonal block-wise transform

Lee

Khan

Kim

et al. 2014

Signal Processing: Image Communication

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In this paper, based on the block (element)-wise inverse Jacket matrix, a unified fast hybrid diagonal block-wise transform (FHDBT) algorithm is proposed. A new fast diagonal block matrix decomposition is made by the matrix product of successively lower order diagonal Jacket matrix and Hadamard matrix. Using a common lower order matrix in the form of 1 1, a fast recursive structure can be developed in the FHDBT, which is able to convert a newly developed discrete cosine transform (DCT)-II, discrete sine transform (DST)-II, discrete Fourier transform (DFT), and Haar-based wavelet transform (HWT). Since these DCT-II, DST-II, DFT, and HWT are widely used in different areas of applications, the proposed FHDBT can be applied to the heterogeneous system requiring several transforms simultaneously. Comparing with pre-existing DCT-II, DST-II, DFT, and HWT, it is shown that the proposed FHDBT exhibits less the complexity as its matrix size gets larger. The proposed algorithm is also well matched to circulant channel matrix. From the numerical experiments, it is shown that a better performance can be achieved by the use of DCT/DST-II compression scheme compared with the DCT-II only compression method. Signal Processing: Image CommunicationThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. , a fast recursive structure can be developed in the FHDBT, which is able to convert a newly developed discrete cosine transform (DCT)-II, discrete sine transform (DST)-II, discrete Fourier transform (DFT), and Haar-based wavelet transform (HWT). Since these DCT-II, DST-II, DFT, and HWT are widely used in different areas of applications, the proposed FHDBT can be applied to the heterogeneous system requiring several transforms simultaneously. Comparing with pre-existing DCT-II, DST-II, DFT, and HWT, it is shown that the proposed FHDBT exhibits less the complexity as its matrix size gets larger. The proposed algorithm is also well matched to circulant channel matrix. From the numerical experiments, it is shown that a better performance can be achieved by the use of DCT/ DST-II compression scheme compared with the DCT-II only compression method.

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“…Research in this domain can be classified into three parts. The first part is the earliest and concerns the reduction of the number of arithmetic operators required for DCT computation [7][8][9][10][11][12][13]. The second research thematic relates to the computation of DCT using multiple constant multiplication schemes [14][15][16][17][18][19][20][21][22][23][24][25] for hardware implementation.…”

Section: Introductionmentioning

confidence: 99%

Optimized Architecture Using a Novel Subexpression Elimination on Loeffler Algorithm for DCT‐Based Image Compression

2012

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The canonical signed digit (CSD) representation of constant coefficients is a unique signed data representation containing the fewest number of nonzero bits. Consequently, for constant multipliers, the number of additions and subtractions is minimized by CSD representation of constant coefficients. This technique is mainly used for finite impulse response (FIR) filter by reducing the number of partial products. In this paper, we use CSD with a novel common subexpression elimination (CSE) scheme on the optimal Loeffler algorithm for the computation of discrete cosine transform (DCT). To meet the challenges of low-power and high-speed processing, we present an optimized image compression scheme based on two-dimensional DCT. Finally, a novel and a simple reconfigurable quantization method combined with DCT computation is presented to effectively save the computational complexity. We present here a new DCT architecture based on the proposed technique. From the experimental results obtained from the FPGA prototype we find that the proposed design has several advantages in terms of power reduction, speed performance, and saving of silicon area along with PSNR improvement over the existing designs as well as the Xilinx core.

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A Fast Recursive Algorithm For Computing The Discrete Cosine Transform

Cited by 75 publications

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An analysis of real-Fourier domain-based adaptive algorithms implemented with the Hartley transform using cosine-sine symmetries

An analysis of real-Fourier domain-based adaptive algorithms implemented with the Hartley transform using cosine-sine symmetries

A fast hybrid Jacket–Hadamard matrix based diagonal block-wise transform

Optimized Architecture Using a Novel Subexpression Elimination on Loeffler Algorithm for DCT‐Based Image Compression

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