A connection between bit-reverse and matrix transpose, hardware and software consequences

A relationship between bit-reverse and matrix transpose, in the context of 2-D fast Fourier transforms (FFTs), is explained. This relationship is shown to be useful for hardware and software implementation of 2-D FFTs based on the row-column algorithm: the bit-reverse operations involved in the row and column 1-D transforms of length N can merge with the matrix transpose in-between, to form a single bit-reverse of length N², which is more efficient than considering these operations separately. The relationship is also the basis of a new bit-reverse algorithm