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Fast computation of the discrete Walsh and Hadamard transforms

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2 Author(s)
Sundararajan, D. ; Dept. of Electr. & Comput. Eng., Concordia Univ., Montreal, Que., Canada ; Ahmad, M.O.

The discrete Walsh and Hadamard transforms are often used in image processing tasks such as image coding, pattern recognition, and sequency filtering. A new discrete Walsh transform (DWT) algorithm is derived in which a modified form of the DWT relation is decomposed into smaller-sized transforms using vectorized quantities. A new sequency-ordered discrete Hadamard transform (DHAT) algorithm is also presented. The proposed approach results in more regular algorithms requiring no independent data swapping and fewer array-index updating and bit-reversal operations. An analysis of the computational complexity and the execution time performance are provided. The results are compared with those of the existing algorithms

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Image Processing, IEEE Transactions on  (Volume:7 ,  Issue: 6 )