The discrete, orthogonal Walsh functions can be generated by a multiplicative iteration equation. Using this iteration equation, an efficient Walsh transform computation algorithm is derived which is analogous to the Cooley-Tukey algorithm for the complex-exponential Fourier transform.

Abstract—Three prime tools of time series processing are convolution, recursive filtering, and the Cooley-Tukey spectral analysis algorithm. These three algorithms can be performed in a single special-purpose device. This device can be a high-speed digital convolver with some additional features which allow it to perform recursive filtering and the Cooley-Tukey algorithm. Recursive filtering requires that the convolver be able to store computed values back into its input. The Cooley-Tukey algorithm can be performed if the convolver has sufficient indexing flexibility. These additional features should not impair significantly the efficiency of the convolver, since its primary function is to calculate dot products, an operation common to all three algorithms.