On the Equivalence Between One-Dimensional Discrete Walsh-Hadamard and Multidimensional Discrete Fourier Transforms

It is shown that the discrete Walsh–Hadamard transform applied to 2ⁿone-dimensional data is equivalent to the discrete n-dimensional Fourier transform applied to the same 2ⁿdata arranged on the binary n-cube. A similar relationship is valid for the generalized discrete Walsh transform suggested by Andrews and Caspari. This relationship explains the theorem concerning the shift invariance of the power spectrum for the Walsh–Hadamard transform and its generalizations.