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In this brief, a generalized mixed-radix (GMR) algorithm is proposed for memory-based fast Fourier transform (FFT) processors to support prime-sized and traditional 2n -point FFTs simultaneously. It transforms the index to a multidimensional vector for efficient computation. By controlling the index vector to satisfy the ??vector reverse?? behavior, the GMR algorithm can support not only in-place policy for both computation and I/O data for continuous data flow to minimize the memory size but also multibank memory structures to increase the maximum throughput without memory conflict. Finally, a low-complexity implementation of an index vector generator is also proposed for our algorithm.