Comparison between Haar and Daubechies Wavelet Transformions on FPGA Technology

Authors: Mohamed I. Mahmoud, Moawad I. M. Dessouky, Salah Deyab, Fatma H. Elfouly

Abstract:

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 comparison between the Haar and Daubechies wavelets is investigated. The Bit Error Rat (BER) between the input audio signal and the reconstructed output signal for each wavelet is calculated. It is seen that the BER using Daubechies wavelet techniques is less than Haar wavelet. The design procedure has been explained and designed using the stat-of-art Electronic Design Automation (EDA) tools for system design on FPGA. Simulation, synthesis and implementation on the FPGA target technology has been carried out.

Keywords: Daubechies wavelet, discrete wavelet transform, Haar wavelet, Xilinx FPGA.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1333124

References:

[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. Wavelet transform No of bits BER Daubechies 16384 0% Haar 16384 46% World Academy of Science, Engineering and Technology 2 200771
[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.