A method and apparatus to reduce the amount of required memory and instruction cycles when implementing Fast Fourier Transforms (FFTs) on a computer system is described. The invention optimizes FFT software using in-place bit reversal (IPBR) implemented on a processor capable of bit reversed incrementation. Alternative embodiments implement the invention for out of place bit reversal (OOPBR) and on processors that do not support special instructions for bit reversed incrementation. The invention only generates unique bit-reversed address pairs and avoids generation of self-reversed addresses. To optimize the invention for in place bit reversal, every non-self bit reversed address in the input array is generated only once, while making simple, computationally efficient increments away from the previous pair of bit reversed addresses. The address pair generator can independently advance only one address in each address pair, and bit reversal of one address uniquely defines the other address.