Browse > Article
http://dx.doi.org/10.5573/ieie.2014.51.9.030

Inverse-Orthogonal Jacket-Haar and DCT Transform  

Park, Ju Yong (Department of Internet, Information & Communication, Shyngyeong University)
Khan, Md. Hashem Ali (Division of Electronic Engineering, Chonbuk National University)
Kim, Jeong Su (Department of Compter, Information & Communication, Korea Soongsil Cyber University)
Lee, Moon Ho (Division of Electronic Engineering, Chonbuk National University)
Publication Information
Journal of the Institute of Electronics and Information Engineers / v.51, no.9, 2014 , pp. 30-40 More about this Journal
Abstract
As the Hadamard transform can be generalized into the Jacket transform, in this paper, we generalize the Haar transform into the Jacket-Haar transform. The entries of the Jacket-Haar transform are 0 and ${\pm}2^k$. Compared with the original Haar transform, the basis of the Jacket-Haar transform is general and more suitable for signal processing. As an application, we present the DCT-II(discrete cosine transform-II) based on $2{\times}2$ Hadamard matrix and HWT(Haar Wavelete transform) based on $2{\times}2$ Haar matrix, analysis the performances of them and estimate them via the Lenna image simulation.
Keywords
Hadamard Transform; Haar Transform; Jacket-Haar Transform; HWT; DCT;
Citations & Related Records
연도 인용수 순위
  • Reference
1 H. F. Harmuth, Transmission of Information by Orthogonal Functions, 2nd ed., Springer-Verlag, Berlin, 1972.
2 S. R. Lee and M. H. Lee, "On the reverse Jacket matrix for weighted Hadamard transform," IEEE Trans. Circuit Syst. II, vol. 45, no. 1, pp. 436-441, March 1998.   DOI   ScienceOn
3 A. K. Louis, P. Maab, and A. Rieder, Wavelets Theory and Applications, John Wiley & Sons, Chichester, 1997.
4 M. H. Lee, B. S. Rajan, and J. Y. Park, "A generalized reverse jacket transform," IEEE Trans. Circuits Syst. II, vol. 48, pp. 684-690, July 2001.   DOI   ScienceOn
5 W. Song, M. H. Lee, and G. Zeng, "Orthogonal space-time block codes design using Jacket transform for MIMO transmission system," IEEE International Conference on Communication, pp. 766-769, 2008.
6 S. C. Pei and J. J. Ding, "Generalizing the Jacket transform by sub orthogonality extension," EUSIOCO, pp. 408-412, Aug. 2009.
7 D.F. Elliot and K.R. Rao, Fast Transforms, Algorithms, Applications, New York: Academic, 1982.
8 N. Ahamed and K.R. Rao, Orthogonal Transform for Digital Signal Processing, Springer-Verlag, 1975.
9 Moon Ho Lee, Jacket Matrices; Construction and Its Applications for Fast Cooperative Wireless Signal Processing, Germany LAMBERT, 2012.
10 M.H. Lee and M. Kaveh, "Fast Hadamard Transform Based on A Simple Matrix Factorization," IEEE Transactions on ASSP. ASSP-34, 1986.
11 Moon Ho Lee, "The Center Weighted Hadamard Transform," IEEE Transactions on Circuit and Systems, 36, 1986
12 R. K. Yarlagadda and J. E. Hershey, Hadamard Matrix Analysis and Synthesis, Kluwer Academic Publishers, 1997.
13 Jesus Gutierrez-Gutierrez, Crespo and M. Pedro, "Block Toeplitz Matrices: Asymptotic Results and Applications," Foundations and Trends(R) in Communications and Information Theory, 8, 2012.
14 W.-H. Chen, C. H. Smith, and S. C. Fralick, "A fast computational algorithm for the discrete cosine transform," IEEE Trans. Commun., vol. 25, no. 9, 1997.
15 H. C. Andrews and K. L. Caspari, "A generalized technique for spectral analysis," IEEE Trans. Computers, vol. 19, no. 1, 1970.
16 J. G. Proakis, Digital Communication, McGraw Hill, 4th Edition, 2000.
17 http://en.wikipedia.org/wiki/Category:Matrices, http://en.wikipedia.org/wiki/Jacket:Matrix, http://en.wikipedia.org/wiki/user:leejacket.