Matrix analysis
Fast Algorithms for Digital Signal Processing
Fast Algorithms for Digital Signal Processing
Number Theory in Digital Signal Processing
Number Theory in Digital Signal Processing
Orthogonal Transforms for Digital Signal Processing
Orthogonal Transforms for Digital Signal Processing
Eigenspaces of the discrete Walsh transform
Problems of Information Transmission
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The discrete Walsh transform is a linear transform defined by a Walsh matrix. Three ways to construct Walsh matrices are known, which differ by the sequence order of rows and correspond to the Paley, Walsh, and Hadamard enumerations. We propose a new enumeration of Walsh matrices and study its properties. The new enumeration is constructed as a linear rearrangement; we obtain an eigenvector basis for it and propose a convenient-to-generate fast implementation algorithm; the new enumeration possesses certain symmetry properties, which make it similar to the discrete Fourier transform.