Is there a FFT algorithm with the circular buffering?
The listed algorithm seems to be form of sliding DFT, summing narrow rectangular slice windows.  In general, an FFT (O(NLogN) is faster than a sliding DFT of slice size b (O(b*N)), for b &gt; LogN , due to a factorization that is not available to slices alone.  Thus, avoiding the 16384 FFT seems to be more expensive than just doing the FFT (if you actually want all 8192 correct bin results), since 256 &gt; log(16384).