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Method of fast 1-D paired transforms for computing the 2D discrete Hadamard transform

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2 Author(s)
A. M. Grigoryan ; Dept. of Electr. Eng., Texas A&M Univ., College Station, TX, USA ; S. S. Agaian

In this brief, two different approaches to compute the 2-D discrete Hadamard transform (DHAT) of sizes 2r×2r , r>1 are presented. Both are based on the so-called 1-D discrete paired transforms, which split the 2r-point DHAT into a set of smaller 2r-1-point transforms, i=1:r. The first approach is a column (row)-wise algorithm which requires, on average, no more than 12 operations of additions per sample. The second approach is a splitting algorithm, in which the 2r×2r-point DHAT is reduced to the computation of 2r-13 1-D DHATs instead of 2r+1 1-D DHAT's in the column (row)-wise algorithm, but requires more operations of additions. Examples and comparison of the proposed algorithms with the known algorithms are provided

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IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing  (Volume:47 ,  Issue: 10 )