Issue No. 02 - February (1970 vol. 19)
R.J. Lechner , Sylvania Electronic Systems
J. L. Shanks<sup>1</sup>has given an algorithm for computing the discrete Walsh transform (abstract Fourier transform) of a sampled periodic function whose domain of definition is the set of integers modulo 2<sup>n</sup>. An algorithm of the same efficiency, using a much simpler notation, was given for the abstract Fourier transform in my correspondence published in 1963 in this TRANSACrIONS.<sup>2</sup>This transform has an identical matrix representation; the only difference is that the function domain is represented (for computation purposes) by binary coded representations of the integers from 0 to 2<sup>n</sup>-1. These binary n-tuples form a group under vector addition, modulo two.
R.J. Lechner, "Comment on "Computation of the Fast Walsh-Fourier Transform"<sup>1</sup>", IEEE Transactions on Computers, vol. 19, no. , pp. 174, February 1970, doi:10.1109/T-C.1970.222890