The Walsh–Hadamard Transforms refer to a series of transforms related to Walsh functions and Hadamard matrix. These transforms have numerous applications in different areas of engineering and science. There are many versions of the Walsh–Hadamard Transform. In this article, the most important versions of the Walsh–Hadamard Transforms are reviewed. We start with the definition of the Walsh functions and finish the article with the Conjugate Symmetric Sequency-Ordered Hadamard Transform.

Walsh–Hadamard Transforms: A Review

Spectral filtering and the computation of Fourier coefficients by the fast Walsh transform (FWT) and the fast algorithm for the real discrete Fourier transform (FRFT) are discussed on a comparative basis. In all cases discussed, the FRFT has fewer multiplications and additions. As the comparisons show, there is no good reason for using the Walsh-Fourier method in spectral filtering or for the generation of Fourier coefficients if the number of operations are the major criterion. However, the Walsh-Fourier method may still be useful if both the Walsh and the Fourier coefficients are to be utilized in a particular application. >

On Walsh-domain versus RDFT filtering

Zarowski and Yunik [1] demonstrated that an FIR filter can be realized with fewer multiplications in the fast Walsh transform (FWT) domain than in the fast Fourier transform (FFT) domain for some transform lengths. This correspondence investigates the symmetry and sparseness of the Walsh gain matrices. An efficient sparse matrix algorithm is used to calculate the Walsh gain matrix.

J. Stoughton

Papers

Further results in Walsh domain filtering