Hybrid Spectral Transform Diagrams

We give a uniform algebraic framework for computing hybrid spectral transforms in an eecient manner. Based on properties of the Kronecker product, we derive a set of recursive equations, which leads naturally to an algorithm for computing such transforms eeciently. As a result, many applications of transforms like the Walsh transform and the Reed-Muller transform, which were previously impossible because of memory constraints, have now become feasible. The same set of recursive equations also gives a new way of explaining hybrid transform diagrams, an eecient data-structure for integer valued boolean functions.