### Economic Power Speed Daubechies Wavelet Filter Using VLSI

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

K. Wahid, V. Dimitrov, and G. Jullien, “VLSI architectures of Daubechies wavelets for algebraic integers,” J. Circuits Syst. Comput., vol. 13, no. 6, pp. 1251–1270, 2013.

K. A. Wahid, V. S. Dimitrov, G. A. Jullien, and W. Badawy, “An algebraic integer based encoding scheme for implementing Daubechies discrete wavelet transforms,” in Proc. Asilomar Conf. Signals, Syst. Comp., 2013, vol. 1, pp. 967–971.

A. Madanayake, R. J. Cintra, D. Onen, V. S. Dimitrov, N. T. Rajapaksha, L. T. Bruton, and A. Edirisuriya, “A row-parallel 8 8 2-D DCT architecture using algebraic integer based exact computation,”IEEE Trans. Circuits Syst. Video Technol., vol. 22, no. 6, pp. 915–929, Jun. 2012.

K. A.Wahid, V. S. Dimitrov, G. A. Jullien, andW. Badawy, “An analysis of Daubechies discrete wavelet transform based on algebraic integer encoding scheme,” in Proc. 3rd Int. Workshop Digital Computational Video DCV 2012, 2002, pp. 27–34.

M. Misiti, Y. Misiti, G. Oppenheim, and J.-M. Poggi, Wavelet Toolbox User’s Guide. New York: Mathworks, Inc., 2011.

A. Madanayake, R. J. Cintra, D. Onen, V. S. Dimitrov, N. T. Rajapaksha, L. T. Bruton, and A. Edirisuriya, “A row-parallel 8 8 2-D DCT architecture using algebraic integer based exact computation,”IEEE 2011

Y.Wu, R. J. Veillette, D. H. Mugler, and T. T. Hartley, “Stability analysis of wavelet-based controller design,” in Proc. Amer. Control Conf. 2001, 2011, vol. 6, pp. 4826–4827.

G. Xing, J.Li, S. Li, andY.-Q.Zhang, “Arbitrarily shaped video-object coding by wavelet,” IEEE Trans. Circuits Syst. Video Technol., vol. 11, no. 10, pp. 1135–1139, Oct. 2011.

K. A. Wahid, V. S. Dimitrov, and G. A. Jullien, “Error-free arithmetic for discrete wavelet transforms using algebraic integers,” in Proc. 16th IEEE Symp. Computer Arithmetic, 2011, pp. 238–244.

S.-C. B. Lo, H. Li, and M. T. Freedman, “Optimization of wavelet decomposition for image compression and feature preservation,” IEEE Trans. Med. Imag., vol. 22, no. 9, pp. 1141–1151, Sep. 2009.

V. S. Dimitrov, G. A. Jullien, andW. C.Miller, “A new DCT algorithm based on encoding algebraic integers,” in Proc. IEEE Int. Conf.

Acoustics,Speech Signal Process., Seattle,WA, 2008, vol. 3, pp. 1377–1380

S. Mallat, A Wavelet Tour of Signal Processing. Burlington, MA:Academic, 2008.

V. Britanak, P. Yip, and K. R. Rao, Discrete Cosine and Sine Transforms. New York: Academic, 2007.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. Cambridge, U.K.: Cambridge Univ.Press, 2006.

R. Baghaie and V. Dimitrov, “Systolic implementation of real-valued discrete transforms via algebraic integer quantize-ation,” Comput. Math. Appl., vol. 41, pp. 1403–1416, 2005

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed. London: Oxford Univ. Press, 2005.

R. A. Games, S. D. O’Neil, and J. J. Rushanan, “Algebraic Integer Quantization and Conversion,” Tech. Rep. NY 13441-5700, July 1988, Rome Air Development Center, Griffiss Air Force Base.

G. Plonka, “A global method for invertible integer DCT and integerwavelet algorithms,” Appl. Comput. Harmonic Anal., vol. 16, no. 2, pp. 79–110, Mar. 2004.

M. Vetterli and J. Kovačević, Wavelets and Subband Coding. Englewood Cliffs, NJ: Prentice Hall PTR, 1995.

G. Dimitroulakos, M. D. Galanis, A. Milidonis, and C. E. Goutis, “A high-throughput and memory efficient 2D discrete wavelet transform hardware architecture for JPEG2000std,” in Proc. IEEE Int.Symp. Circuits Syst. ISCAS 2005, 2005, pp.

S. Mallat, A Wavelet Tour of Signal Processing. Burlington, MA:Academic, 2008.

D. Tay and N. Kingsbury, “Design of nonseparable 3-D filter banks/wavelet bases using transformations of variables.,” IEEE Proc. Visual Image Signal Process., vol. 143, pp. 51–61, 1996

S. Murugesan and D. B. H. Tay, “New techniques for rationalizing orthogonal and biorthogonal wavelet filter coefficients,” IEEE Trans.Circuits Syst., vol. 59, no. 3, pp. 628–637, Mar. 2002.

J. Cozzens and L. Finkelstein, “Computing the discrete Fourier Trans- form using residue number systems in a ring of algebraic integers,”IEEE Trans. Inf. Theory, vol. 31, no. 5, pp. 580–588, 2002.

R. Dedekind, Theory of Algebraic Integers, J. Stillwell, Ed. Cambridge: Cambridge Univ. Press, Sep. 1998.

### Refbacks

- There are currently no refbacks.

This work is licensed under a Creative Commons Attribution 3.0 License.