Modified Fast and Exact Algorithm for Fast Haar Transform
Wavelet transform or wavelet analysis is a recently
developed mathematical tool in applied mathematics. In numerical
analysis, wavelets also serve as a Galerkin basis to solve partial
differential equations. Haar transform or Haar wavelet transform has
been used as a simplest and earliest example for orthonormal wavelet
transform. Since its popularity in wavelet analysis, there are several
definitions and various generalizations or algorithms for calculating
Haar transform. Fast Haar transform, FHT, is one of the algorithms
which can reduce the tedious calculation works in Haar transform. In
this paper, we present a modified fast and exact algorithm for FHT,
namely Modified Fast Haar Transform, MFHT. The algorithm or
procedure proposed allows certain calculation in the process
decomposition be ignored without affecting the results.
[1] A.W. Galli, G.T. Heydt, and P.F. Ribeiro, "Exploring the power of
wavelet analysis." IEEE Computer Application in Power, pp.37 - 41,
Oct 1996.
[2] M.N.O. Sadiku, C.M. Akujuobi, and R.C. Garcia, "An introduction to
wavelets in electromagnetics." Microwave Magazine, IEEE, vol.
6(2), pp. 63 - 72, June 2005.
[3] G.P. Nason, "A little introduction to wavelets." Applied Statistical
Pattern Recognition, IEEE Colloquium on 20 April 1999, pp.1 - 6, April
1999.
[4] E. Aboufadel and S. Schlicker, Discovering Wavelets, New York: John
Wiley & sons, Inc, pp. 12-18, 1999.
[5] P. R. Roeser and M.E. Jernigan, "Fast Haar transform algorithms" IEEE
Transcations on Computer, vol. c-31, pp. 175-177, Feb 1982.
[6] R. S. Stankovic and B. J. Falkowski, "The Haar wavelet transform: its
status and achievements" Computers and Electrical Engineering, vol. 29,
pp. 25-44, 2003.
[7] G. Kaiser, "The fast Haar transform. Gateway to wavelet." Potentials,
IEEE, vol. 17(2), pp 34-37, April-May 1998.
[1] A.W. Galli, G.T. Heydt, and P.F. Ribeiro, "Exploring the power of
wavelet analysis." IEEE Computer Application in Power, pp.37 - 41,
Oct 1996.
[2] M.N.O. Sadiku, C.M. Akujuobi, and R.C. Garcia, "An introduction to
wavelets in electromagnetics." Microwave Magazine, IEEE, vol.
6(2), pp. 63 - 72, June 2005.
[3] G.P. Nason, "A little introduction to wavelets." Applied Statistical
Pattern Recognition, IEEE Colloquium on 20 April 1999, pp.1 - 6, April
1999.
[4] E. Aboufadel and S. Schlicker, Discovering Wavelets, New York: John
Wiley & sons, Inc, pp. 12-18, 1999.
[5] P. R. Roeser and M.E. Jernigan, "Fast Haar transform algorithms" IEEE
Transcations on Computer, vol. c-31, pp. 175-177, Feb 1982.
[6] R. S. Stankovic and B. J. Falkowski, "The Haar wavelet transform: its
status and achievements" Computers and Electrical Engineering, vol. 29,
pp. 25-44, 2003.
[7] G. Kaiser, "The fast Haar transform. Gateway to wavelet." Potentials,
IEEE, vol. 17(2), pp 34-37, April-May 1998.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56388", author = "Phang Chang and Phang Piau", title = "Modified Fast and Exact Algorithm for Fast Haar Transform", abstract = "Wavelet transform or wavelet analysis is a recently
developed mathematical tool in applied mathematics. In numerical
analysis, wavelets also serve as a Galerkin basis to solve partial
differential equations. Haar transform or Haar wavelet transform has
been used as a simplest and earliest example for orthonormal wavelet
transform. Since its popularity in wavelet analysis, there are several
definitions and various generalizations or algorithms for calculating
Haar transform. Fast Haar transform, FHT, is one of the algorithms
which can reduce the tedious calculation works in Haar transform. In
this paper, we present a modified fast and exact algorithm for FHT,
namely Modified Fast Haar Transform, MFHT. The algorithm or
procedure proposed allows certain calculation in the process
decomposition be ignored without affecting the results.", keywords = "Fast Haar Transform, Haar transform, Wavelet
analysis.", volume = "1", number = "11", pages = "542-4", }