Abstract: A multi-dimensional transformer for a group of input coefficients representative of a signal or signals with a single transformer and two transpose buffers is described. A two-dimensional transform is performed by a multiplexer and a single one-dimensional transformer. In addition, the one-dimensional transformer preferably includes two separate processors, each performing part of the one-dimensional transform. Each processor may suitably be constructed of a number of primary cells, each of which includes a multiplier, addition circuit, and a register. The registers of the primary cells are connected together in a circular manner. Alternatively, a partial product circuit can be provided in place of the multipliers.