A Digit Reversal Circuit for the Variable-Length Radix-4 FFT

When the fast Fourier transform (FFT) is executed using an in-place method, the input or output data must be accessed in a digit-reversed order. The previous digit reversal circuits, which are based on a binary counter, require complex multiplexers. This paper proposes a new digit reversal circuit based on two-bit counter modules for the variable-length radix-4 FFT. This circuit can be designed with minimal multiplexers, and thus can efficiently generate digit-reversed sequences compared with digit reversal circuits based on a binary counter.