SPLIT MULTIPLE RADIX FFT

In the paper general rules for construction of splitradix FFTs having multiple auxiliary bases is presented. The algorithms exist for DFT sizes being products of mutually prime numbers. The algorithms have smaller arithmetical and multiplicative complexities than simpler FFTs, parameters allowing comparison are also introduced. The obtained results are remarkable, some of FFTs have smaller arithmetical, or at least multiplicative complexities than “standard” split-radix FFT. When compared to other algorithms for such
$N$
savings in the numbers of arithmetical operations emerge even for the smallest useful DFT sizes. The presented techniques provides new tools for construction of optimized FFTs, e.g. DFT modules for very large radix algorithms generated by automatic software, like FFTW.