Because of the rapid advances in multiplication hardware, the most time consuming processing step in Fourier Transform will be the number of memory accesses rather than the number of multiplications. An algorithm of Continuous Fourier Transform (CFT) which minimizes memory access was developed. It can be implemented with existing technology and is potentially faster than FFT, particularly for processing continuous, real-time signals.
"Fourier Transform Faster Than Fast Fourier Transform (FFT)", Proc. SPIE 0241, Real-Time Signal Processing III, (24 December 1980); doi: 10.1117/12.959241; https://doi.org/10.1117/12.959241