The recursive implementation of the radix-2 Decimation-In-Frequency algorithm can be understood using the following two figures.
The first one refers to pushing the stack phase, while the second one illustrates the popping the stack phase.
In particular, the two figures illustrate the Matlab implementation that you may find on our GitHub website:
The above recursive implementation is the counterpart of the iterative implementation of the radix-2 Decimation In Frequency. Please, note that the present recursive one does not require any reverse bit ordering, neither of the input nor of the output sequences.