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

In this brief, two different approaches to compute the 2-D discrete Hadamard transform (DHAT) of sizes 2^r×2^r , r>1 are presented. Both are based on the so-called 1-D discrete paired transforms, which split the 2^r-point DHAT into a set of smaller 2^r-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 2^r×2^r-point DHAT is reduced to the computation of 2^r-13 1-D DHATs instead of 2^r+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