Comparison between Haar and Daubechies Wavelet Transformations on FPGA Technology

Recently, the Field Programmable Gate Array (FPGA) technology offers the potential of designing high performance systems at low cost. The discrete wavelet transform has gained the reputation of being a very effective signal analysis tool for many practical applications. However, due to its computation-intensive nature, current implementation of the transform falls short of meeting real-time processing requirements of most application. The objectives of this paper are implement the Haar and Daubechies wavelets using FPGA technology. In addition, the Bit Error Rate (BER) between the input audio signal and the reconstructed output signal for each wavelet is calculated. From the BER, it is seen that the implementations execute the operation of the wavelet transform correctly and satisfying the perfect reconstruction conditions. The design procedure has been explained and designed using the stat-ofart Electronic Design Automation (EDA) tools for system design on FPGA. Simulation, synthesis and implementation on the FPGA target technology has been carried out.

• Fatma H. Elfouly
• Mohamed I. Mahmoud
• Moawad I. M. Dessouky
• Salah Deyab

• Daubechies wavelet
• discrete wavelet transform
• Haar wavelet
• Xilinx FPGA.

[1] Ali, M., 2003. Fast Discrete Wavelet Transformation Using FPGAs and
Distributed Arithmetic. International Journal of Applied Science and
Engineering, 1, 2: 160-171.
[2] Riol, O. and Vetterli, M. 1991 Wavelets and signal processing. IEEE
Signal Processing Magazine, 8, 4: 14-38.
[3] Beylkin, G., Coifman, R., and Rokhlin,V. 1992.Wavelets in Numerical
Analysis in Wavelets and Their Applications. New York: Jones and
Bartlett, 181-210.
[4] Field, D. J. 1999. Wavelets, vision and the statistics of natural scenes.
Philosophical Transactions of the Royal Society: Mathematical, Physical
and Engineering Sciences, 357, 1760: 2527-2542.
[5] Antonini, M., Barlaud, M., Mathieu, P., and Daubechies, I.1992.Image
coding using wavelet transform.IEEE Transactions on Image Processing,
1, 2: 205-220.
[6] Knowles, G. 1990. VLSI architecture for the discrete wavelet transform.
Electron Letters, 26, 15: 1184-1185.
[7] Parhi, K. and Nishitani, T. 1993.VLSI architectures for discrete wavelet
transforms. IEEE Transactions on VLSI Systems, 191-202.
[8] Chakabarti, C. and Vishwanath, M. 1995. Efficient realizations of the
discrete and continuous wavelet transforms: from single chip
implementations to mappings on SIMD array computers. IEEE
Transactions on Signal Processing , 43, 3: 759-771.
[9] Seals, R. and Whapshott, G. 1997. Programmable Logic: PLDs and
FPGAs. UK: Macmillan.
[10] Nick, K. and Julian, M. 1997. Wavelet Transform in Image Processing.
Signal Processing and Prediction I, Eurasip, ICT press, 23-34.
[11] James S. Walker. 1999. A Primer on Wavelets and Scientific
Applications.
[12] Applying the Haar Wavelet Transform to Time Series Information
[13] HDL Designer Series User Manual, Software Version 2003.1,9 April
2003, Mentor Graphics Corporation 1996-2003.
[14] Modelsim 5.6 SE Performance Guidelines, Model Technology February
2002, User-s Manual, Version 5.6e, Mentor Graphics Corporation 1996-
2002.
[15] Lenardo Spectrum User-s Manual, Mentor Graphics Corporation 1990-
2003.
[16] Vaidyanathan, P. 1993. Multirate Systems and Filter Banks. New Jersey:
Prentice Hall.