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Tree structures for computing orthogonal transforms are introduced. Two cases, delay trees and decimation trees, are investigated. A simple condition, namely the orthogonality of branches with a common root, is shown to be necessary and sufficient for the overall transform to be orthogonal. Main advantages are structural simplicity and a number of operations proportional to N Log2N. Application of the tree structures to the Walsh-Hadamard Transform (in natural, sequency and dyadic order) is presented. A single module can be multiplexed or used in parallel in order to perform all operations. Such a system is shown to be well suited for hardware implementation.
Laurent Villard, Stephan Brunner, Alberto Bottino, Moahan Murugappan
Martin Alois Rohrmeier, Johannes Hentschel, Gabriele Cecchetti, Sabrina Laneve, Ludovica Schaerf