A reconfigurable architecture for and method of performing a fast orthogonal transform of vectors in multiple stages, the size of a vector being N, wherein N can vary and the number of stages is a function of N, the architecture comprising: a computational unit configured and arranged so as to include one or more butterfly units; a block including one or more multipliers coupled to the output of the computational unit, configured and arranged so as to perform all of the butterfly computations for at least one stage of the transform; a storage unit configured and arranged so as to store the intermediate results of the butterfly computations and predetermined coefficients for use by the computational unit for performing each butterfly computation, the storage unit including memory and multiplexing architecture; the storage unit including memory and multiplexing architecture; a multiplexer unit configured and arranged so as to time multiplex all of the butterfly computations of the transform using said computation unit for the one stage so that only one computation unit is required for the stage; and a controller configured and arranged so as to provide coefficients to the computational unit, and control the sizes of memory and multiplexing architecture in the storage unit; wherein the multipliers' coefficients, the coefficients of the computational unit, the sizes of memories, and multiplexing architecture, for each stage are modified as a function of the value of N. The architecture can be implemented as an integrated chip, and used in communication devices.