On fast hadamard transforms of Williamson type

The Hadamard transform of Sylvester's type, which is also known as the Walsh-Hadamard transform, is widely used in signal processing and communication. Note that the Walsh-Hadamard transform operates only with vectors whose length AT is a power of 2. If N is not a power of two, then in order to compute the Walsh-Hadamard spectrum of the vector one has to either discard components or pad zeros up to the next power of two. In the first case we have an information loss and in the second case extra computations are needed. Thus, construction of fast Hadamard transforms of different orders is important problem. In this paper we develop fast Hadamard transforms based on special classes of Hadamard matrices, namely, the Williamson type Hadamard matrices.