Hardware Implementation of Fast Recursive Walsh-Hadamard Transform

Authors

  • Mazumder P Department of Electronics and Communication Engineering, Regent Education and Research Foundation, Kolkata 700121, India
  • Middya R Department of Electronics and Telecommunication Engineering, Jadavpur University, Kolkata 700032, India
  • Naskar MK

Keywords:

Signal processing, VLSI, FFT, Transforms

Abstract

The Walsh Hadamard Transform is an extremely relevant concept in modern digital image data compression. This paper examines the feasibility of using a tensor product based approach to Walsh Hadamard Transfrom for implementation to hardware architecture using FPGA technology. This paper explains the derivation of a highly parallel and very fast algorithm for the computation of both one-dimensional and two-dimensional transforms using tensor product. Such a fast dedicated hardware design for the Walsh Hadamard Transform will help a wide range of digital signal processing applications.

References

[1] J. Granata, M. Conner, R. Tolimieri, “Recursive fast algorithm and the role of the tensor product,” IEEE Transactions on Signal Processing, vol. 40, no. 12, pp. 2921–2930, Dec 1992.

[2] J. R. Johnson, R. W. Johnson, D. Rodriguez, and R. Tolimieri, “A methodology for designing, modifying, and implementing fourier transform algorithms on various architectures,” Circuits, Systems and Signal Processing, vol. 9, no. 4, pp. 449–500, Dec 1990.

[3] D. F. Chiper, “Radix-2 fast algorithm for computing discrete hartley trans- form of type iii,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 59, no. 5, pp. 297–301, May 2012.

[4] D. F. Chiper, “A novel vlsi dht algorithm for a highly modular and parallel archi- tecture,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 60, no. 5, pp. 282–286, May 2013.

[5] M. T. Hamood and S. Boussakta, “Fast walsh-hadamard-fourier transform algorithm,” IEEE Transactions on Signal Processing, vol. 59, no. 11, pp. 5627–5631, Nov 2011.

[6] J. R. Johnson and A. F. Breitzman, “Automatic derivation and implemen- tation of fast convolution algorithms,” Journal of Symbolic Computation, vol. 37, no. 2, pp. 261 – 293, 2004.

[7] M. A. Richard Tolimieri and C. Lu, Algorithms for Discrete Fourier Transform and Convolution. Springer-Verlag New York, 1997.

Downloads

Published

2025-11-24

How to Cite

[1]
P. Mazumder, R. Middya, and M. K. Naskar, “Hardware Implementation of Fast Recursive Walsh-Hadamard Transform”, Int. J. Comp. Sci. Eng., vol. 7, no. 1, pp. 28–32, Nov. 2025.