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Journal articles on the topic 'Discrete cosine transforms (DCTs)'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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1

Rad, Farhad, and Ali Broumandnia. "An Efficient Implementation of the Entire Transforms in the H.264/AVC Encoder using VHDL." International Journal of Reconfigurable and Embedded Systems (IJRES) 2, no. 3 (November 1, 2013): 116. http://dx.doi.org/10.11591/ijres.v2.i3.pp116-121.

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The H.264/AVC standard achieves remarkable higher compression performance than the previous MPEG and H.26X standards. One of the computationally intensive units in the MPEG and H.26X video coding families is the Discrete Cosine Transform (DCT). In this paper, we propose an efficient implementation of the DCT, inverse DCTs and the Hadamard transforms in the H.264/AVC encoder using VHDL. The synthesis results indicate that our implementation of the entire transforms achieves lower power, delay and area consumption compared to the existing architectures in the H.264/AVC encoder.

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2

Kim, Donyeon. "Fast algorithm for discrete cosine transform (DCT)-domain image downsampling using Winograd DCTs." Optical Engineering 42, no. 9 (September 1, 2003): 2485. http://dx.doi.org/10.1117/1.1599842.

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3

Tsai, S. E., and S. M. Yang. "A Fast DCT Algorithm for Watermarking in Digital Signal Processor." Mathematical Problems in Engineering 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/7401845.

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Discrete cosine transform (DCT) has been an international standard in Joint Photographic Experts Group (JPEG) format to reduce the blocking effect in digital image compression. This paper proposes a fast discrete cosine transform (FDCT) algorithm that utilizes the energy compactness and matrix sparseness properties in frequency domain to achieve higher computation performance. For a JPEG image of8×8block size in spatial domain, the algorithm decomposes the two-dimensional (2D) DCT into one pair of one-dimensional (1D) DCTs with transform computation in only 24 multiplications. The 2D spatial data is a linear combination of the base image obtained by the outer product of the column and row vectors of cosine functions so that inverse DCT is as efficient. Implementation of the FDCT algorithm shows that embedding a watermark image of 32 × 32 block pixel size in a 256 × 256 digital image can be completed in only 0.24 seconds and the extraction of watermark by inverse transform is within 0.21 seconds. The proposed FDCT algorithm is shown more efficient than many previous works in computation.

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4

Kliuchenia, V. V. "Design of a discrete сosine transformation processor for image compression systems on a losless-to-lossy circuit." Doklady BGUIR 19, no. 3 (June 2, 2021): 5–13. http://dx.doi.org/10.35596/1729-7648-2021-19-3-5-13.

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Today, mobile multimedia systems that use the H.261 / 3/4/5, MPEG-1/2/4 and JPEG standards for encoding / decoding video, audio and images are widely spread [1–4]. The core of these standards is the discrete cosine transform (DCT) of I, II, III ... VIII types [DCT]. Wide support in a huge number of multimedia applications of the JPEG format by circuitry and software solutions and the need for image coding according to the L2L scheme determines the relevance of the problem of creating a decorrelated transformation based on DCT and methods for rapid prototyping of processors for computing an integer DCT on programmable systems on a FPGA chip. At the same time, such characteristics as structural regularity, modularity, high computational parallelism, low latency and power consumption are taken into account. Direct and inverse transformation should be carried out according to the “whole-to-whole” processing scheme with preservation of the perfective reconstruction of the original image (the coefficients are represented by integer or binary rational numbers; the number of multiplication operations is minimal, if possible, they are excluded from the algorithm). The wellknown integer DCTs (BinDCT, IntDCT) do not give a complete reversible bit to bit conversion. To encode an image according to the L2L scheme, the decorrelated transform must be reversible and implemented in integer arithmetic, i. e. the conversion would follow an “integer-to-integer” processing scheme with a minimum number of rounding operations affecting the compactness of energy in equivalent conversion subbands. This article shows how, on the basis of integer forward and inverse DCTs, to create a new universal architecture of decorrelated transform on FPGAs for transformational image coding systems that operate on the principle of “lossless-to-lossy” (L2L), and to obtain the best experimental results for objective and subjective performance compared to comparable compression systems.

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5

Jang, Ju-wook, Chang-hyeon Lim, Ronald Scrofano, and Viktor K. Prasanna. "Energy-Efficient Discrete Cosine Transform on FPGAs." KIPS Transactions:PartA 12A, no. 4 (August 1, 2005): 313–20. http://dx.doi.org/10.3745/kipsta.2005.12a.4.313.

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6

Hayati, Raisah, and Rahmadi Kurnia. "Simulasi Unjuk Kerja Discrete Wavelet Transform (DWT) dan Discrete Cosine Transform (DCT) untuk Pengolahan Sinyal Radar di Daerah yang Ber-Noise Tinggi." Jurnal Nasional Teknik Elektro 3, no. 1 (March 1, 2014): 32–43. http://dx.doi.org/10.20449/jnte.v3i1.53.

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7

R., Ononiwu, and Okengwu U. "Efficient Steganography on Video File using Discrete Cosine Transform Method (DCTM)." International Journal of Computer Applications 176, no. 11 (April 15, 2020): 22–28. http://dx.doi.org/10.5120/ijca2020920051.

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8

Bouguezel, Saad, M. Omair Ahmad, and M. N. S. Swamy. "Binary Discrete Cosine and Hartley Transforms." IEEE Transactions on Circuits and Systems I: Regular Papers 60, no. 4 (April 2013): 989–1002. http://dx.doi.org/10.1109/tcsi.2012.2224751.

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9

Domínguez-Jiménez, María Elena, David Luengo, and Gabriela Sansigre-Vidal. "Estimation of Symmetric Channels for Discrete Cosine Transform Type-I Multicarrier Systems: A Compressed Sensing Approach." Scientific World Journal 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/151370.

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The problem of channel estimation for multicarrier communications is addressed. We focus on systems employing the Discrete Cosine Transform Type-I (DCT1) even at both the transmitter and the receiver, presenting an algorithm which achieves an accurate estimation of symmetric channel filters using only a small number of training symbols. The solution is obtained by using either matrix inversion or compressed sensing algorithms. We provide the theoretical results which guarantee the validity of the proposed technique for the DCT1. Numerical simulations illustrate the good behaviour of the proposed algorithm.

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10

Domínguez-Jiménez, María Elena. "Full spark of even discrete cosine transforms." Signal Processing 176 (November 2020): 107632. http://dx.doi.org/10.1016/j.sigpro.2020.107632.

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11

Sanchez, V., P. Garcia, A. M. Peinado, J. C. Segura, and A. J. Rubio. "Diagonalizing properties of the discrete cosine transforms." IEEE Transactions on Signal Processing 43, no. 11 (1995): 2631–41. http://dx.doi.org/10.1109/78.482113.

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12

Soo-Chang Pei and Min-Hung Yeh. "The discrete fractional cosine and sine transforms." IEEE Transactions on Signal Processing 49, no. 6 (June 2001): 1198–207. http://dx.doi.org/10.1109/78.923302.

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13

Chan, Y. H., and W. C. Siu. "Algorithm for prime length discrete cosine transforms." Electronics Letters 26, no. 3 (1990): 206. http://dx.doi.org/10.1049/el:19900139.

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14

Reju, V. G., Soo Ngee Koh, and Ing Yann Soon. "Convolution Using Discrete Sine and Cosine Transforms." IEEE Signal Processing Letters 14, no. 7 (July 2007): 445–48. http://dx.doi.org/10.1109/lsp.2006.891312.

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15

Feig, Ephraim, and Elliot Linzer. "The multiplicative complexity of discrete cosine transforms." Advances in Applied Mathematics 13, no. 4 (December 1992): 494–503. http://dx.doi.org/10.1016/0196-8858(92)90023-p.

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16

Hyesook Lim, V. Piuri, and E. E. Swartzlander. "A serial-parallel architecture for two-dimensional discrete cosine and inverse discrete cosine transforms." IEEE Transactions on Computers 49, no. 12 (2000): 1297–309. http://dx.doi.org/10.1109/12.895848.

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17

CHEN, Bo, Hong-Xia WANG, and Li-Zhi CHENG. "Fast Directional Discrete Cosine Transforms Based Image Compression." Journal of Software 22, no. 4 (June 21, 2011): 826–32. http://dx.doi.org/10.3724/sp.j.1001.2011.03805.

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18

Raguraman, M. Thiruveni, and D. Shanthi Saravanan. "FPGA Implementation of Approximate 2D Discrete Cosine Transforms." Circuits and Systems 07, no. 04 (2016): 434–45. http://dx.doi.org/10.4236/cs.2016.74037.

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19

Liu, Zhengjun, Qing Guo, and Shutian Liu. "The discrete fractional random cosine and sine transforms." Optics Communications 265, no. 1 (September 2006): 100–105. http://dx.doi.org/10.1016/j.optcom.2006.03.010.

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20

Feig, E., and S. Winograd. "On the multiplicative complexity of discrete cosine transforms." IEEE Transactions on Information Theory 38, no. 4 (July 1992): 1387–91. http://dx.doi.org/10.1109/18.144722.

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21

Zhongde Wang. "On computing the discrete Fourier and cosine transforms." IEEE Transactions on Acoustics, Speech, and Signal Processing 33, no. 5 (October 1985): 1341–44. http://dx.doi.org/10.1109/tassp.1985.1164710.

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22

Wang, H., and H. Yan. "Adaptive gabor discrete cosine transforms for image compression." Electronics Letters 28, no. 18 (1992): 1755. http://dx.doi.org/10.1049/el:19921117.

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23

Kouda, Takaharu. "Super-Resolution using Discrete Cosine Transform sign as Index of High-Frequency Components." Journal of The Institute of Image Information and Television Engineers 66, no. 11 (2012): J420—J425. http://dx.doi.org/10.3169/itej.66.j420.

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24

Sherlock, B. G., and Y. P. Kakad. "Windowed discrete cosine and sine transforms for shifting data." Signal Processing 81, no. 7 (July 2001): 1465–78. http://dx.doi.org/10.1016/s0165-1684(01)00033-0.

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25

Chung, Kuo-Liang, and Wen-Ming Yan. "On matrix factorizations for recursive pruned discrete cosine transforms." Signal Processing 68, no. 2 (July 1998): 175–82. http://dx.doi.org/10.1016/s0165-1684(98)00071-1.

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26

Plonka, Gerlind, and Manfred Tasche. "Fast and numerically stable algorithms for discrete cosine transforms." Linear Algebra and its Applications 394 (January 2005): 309–45. http://dx.doi.org/10.1016/j.laa.2004.07.015.

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27

Jar-Ferr Yang and Chih-Peng Fan. "Recursive discrete cosine transforms with selectable fixed-coefficient filters." IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 46, no. 2 (1999): 211–16. http://dx.doi.org/10.1109/82.752956.

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28

Martucci, S. A. "Symmetric convolution and the discrete sine and cosine transforms." IEEE Transactions on Signal Processing 42, no. 5 (May 1994): 1038–51. http://dx.doi.org/10.1109/78.295213.

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29

Muddhasani, Venkatram, and Meghanad D. Wagh. "Bilinear algorithms for discrete cosine transforms of prime lengths." Signal Processing 86, no. 9 (September 2006): 2393–406. http://dx.doi.org/10.1016/j.sigpro.2005.10.022.

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30

Garcia, Stephan Ramon, and Samuel Yih. "Supercharacters and the discrete Fourier, cosine, and sine transforms." Communications in Algebra 46, no. 9 (February 26, 2018): 3745–65. http://dx.doi.org/10.1080/00927872.2018.1424866.

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31

Ersoy, O. "On relating discrete Fourier, sine, and symmetric cosine transforms." IEEE Transactions on Acoustics, Speech, and Signal Processing 33, no. 1 (February 1985): 219–22. http://dx.doi.org/10.1109/tassp.1985.1164506.

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32

Hrivnák, Jiří, and Lenka Motlochová. "Discrete cosine and sine transforms generalized to honeycomb lattice." Journal of Mathematical Physics 59, no. 6 (June 2018): 063503. http://dx.doi.org/10.1063/1.5027101.

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33

Hong, Jonathan. "Discrete Fourier, Hartley, and cosine transforms in signal processing." Signal Processing 37, no. 2 (May 1994): 306. http://dx.doi.org/10.1016/0165-1684(94)90117-1.

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34

Arce-Nazario, Rafael A., Manuel Jiménez, and Domingo Rodríguez. "Mapping of Discrete Cosine Transforms onto Distributed Hardware Architectures." Journal of Signal Processing Systems 53, no. 3 (June 3, 2008): 367–82. http://dx.doi.org/10.1007/s11265-008-0239-x.

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35

Ahmed, S. M., A. F. Al-Ajlouni, M. Abo-Zahhad, and B. Harb. "ECG signal compression using combined modified discrete cosine and discrete wavelet transforms." Journal of Medical Engineering & Technology 33, no. 1 (January 2009): 1–8. http://dx.doi.org/10.1080/03091900701797453.

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36

M. Ahmed, Sabah. "ECG SIGNAL COMPRESSION USING COMBINED MODIFIED DISCRETE-COSINE AND DISCRETE-WAVELET TRANSFORMS." JES. Journal of Engineering Sciences 34, no. 1 (January 1, 2006): 215–26. http://dx.doi.org/10.21608/jesaun.2006.110107.

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37

Hayat, Khizar, and Tanzeela Qazi. "Forgery detection in digital images via discrete wavelet and discrete cosine transforms." Computers & Electrical Engineering 62 (August 2017): 448–58. http://dx.doi.org/10.1016/j.compeleceng.2017.03.013.

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38

ZHELUDEV, VALERY A., DAN D. KOSLOFF, and EUGENE Y. RAGOZA. "COMPRESSION OF SEGMENTED 3D SEISMIC DATA." International Journal of Wavelets, Multiresolution and Information Processing 02, no. 03 (September 2004): 269–81. http://dx.doi.org/10.1142/s0219691304000536.

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We present a preliminary investigation of compression of segmented 3D seismic volumes for the rendering purposes. Promising results are obtained on the base of 3D discrete cosine transforms followed by the SPIHT coding scheme. An accelerated version of the algorithm combines 1D discrete cosine transform in vertical direction with the 2D wavelet transform of horizontal slices. In this case the SPIHT scheme is used for coding the mixed sets of cosine-wavelet coefficients.

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39

Brus, Adam, Jiří Hrivnák, and Lenka Motlochová. "Connecting (Anti)Symmetric Trigonometric Transforms to Dual-Root Lattice Fourier–Weyl Transforms." Symmetry 13, no. 1 (December 31, 2020): 61. http://dx.doi.org/10.3390/sym13010061.

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Explicit links of the multivariate discrete (anti)symmetric cosine and sine transforms with the generalized dual-root lattice Fourier–Weyl transforms are constructed. Exact identities between the (anti)symmetric trigonometric functions and Weyl orbit functions of the crystallographic root systems A1 and Cn are utilized to connect the kernels of the discrete transforms. The point and label sets of the 32 discrete (anti)symmetric trigonometric transforms are expressed as fragments of the rescaled dual root and weight lattices inside the closures of Weyl alcoves. A case-by-case analysis of the inherent extended Coxeter–Dynkin diagrams specifically relates the weight and normalization functions of the discrete transforms. The resulting unique coupling of the transforms is achieved by detailing a common form of the associated unitary transform matrices. The direct evaluation of the corresponding unitary transform matrices is exemplified for several cases of the bivariate transforms.

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40

Cruz-Roldan, Fernando, María Elena Dominguez-Jimenez, Gabriela Sansigre Vidal, Pedro Amo-Lopez, Manuel Blanco-Velasco, and Ángel Bravo-Santos. "On the Use of Discrete Cosine Transforms for Multicarrier Communications." IEEE Transactions on Signal Processing 60, no. 11 (November 2012): 6085–90. http://dx.doi.org/10.1109/tsp.2012.2210714.

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41

Nikara, Jari A., Jarmo H. Takala, and Jaakko T. Astola. "Discrete cosine and sine transforms—regular algorithms and pipeline architectures." Signal Processing 86, no. 2 (February 2006): 230–49. http://dx.doi.org/10.1016/j.sigpro.2005.05.014.

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42

Astola, J., and D. Akopian. "Architecture-oriented regular algorithms for discrete sine and cosine transforms." IEEE Transactions on Signal Processing 47, no. 4 (April 1999): 1109–24. http://dx.doi.org/10.1109/78.752608.

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43

Chang, L. W., and M. C. Wu. "A unified systolic array for discrete cosine and sine transforms." IEEE Transactions on Signal Processing 39, no. 1 (1991): 192–94. http://dx.doi.org/10.1109/78.80779.

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44

Zeng, Bing, and Jingjing Fu. "Directional Discrete Cosine Transforms—A New Framework for Image Coding." IEEE Transactions on Circuits and Systems for Video Technology 18, no. 3 (March 2008): 305–13. http://dx.doi.org/10.1109/tcsvt.2008.918455.

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45

Zhuang, Ling, Lu Liu, Jibi Li, Kai Shao, and Guangyu Wang. "Discrete Sine and Cosine Transforms in Single Carrier Modulation Systems." Wireless Personal Communications 78, no. 2 (May 7, 2014): 1313–29. http://dx.doi.org/10.1007/s11277-014-1819-7.

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46

Clary, S., and D. H. Mugler. "Eigenvectors for a Class of Discrete Cosine and Sine Transforms." Sampling Theory in Signal and Image Processing 3, no. 1 (January 2004): 83–94. http://dx.doi.org/10.1007/bf03549406.

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47

Ta, N., Y. Attikiouzel, and G. Crebbin. "Fast computation of two-dimensional discrete cosine transforms using fast discrete radon transform." Electronics Letters 27, no. 1 (January 3, 1991): 82–84. http://dx.doi.org/10.1049/el:19910053.

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48

Ezhilarasi, R., K. Venkatalakshmi, and B. Pradeep Khanth. "Enhanced approximate discrete cosine transforms for image compression and multimedia applications." Multimedia Tools and Applications 79, no. 13-14 (May 21, 2018): 8539–52. http://dx.doi.org/10.1007/s11042-018-5960-2.

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49

Orea-Flores, I., M. A. Acevedo, and J. López-Bonilla. "Wavelet and discrete cosine transforms for inserting information into BMP images." ANZIAM Journal 48, no. 1 (July 2006): 23–35. http://dx.doi.org/10.1017/s1446181100003394.

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AbstractIn this work we use the Discrete Wavelet Transform in watermarking applications for digital BMP images with the objective is to guarantee some level of security for the copyright. We also compare the results with the Discrete Cosine Transform for the same application. Results are obtained from a number of tests, primarily in order to validate the security level and the robustness of the watermark, but also to prove that the original image suffers only very small variations after the watermark is embedded. We also show how to embed the watermark, where to insert it and the capacity supported for inserting an image.

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50

Wang, Hang. "Efficient image coding method based on adaptive Gabor discrete cosine transforms." Journal of Electronic Imaging 2, no. 1 (January 1, 1993): 38. http://dx.doi.org/10.1117/12.134251.

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