SPLIT VECTOR-RADIX FAST FOURIER-TRANSFORM

The split-radix approach for computing the discrete Fourier transform (DFT) is extended for the vector-radix fast Fourier transform (FFT) to two and higher dimensions. It is obtained by further splitting the (N/2 x N/2) transforms with twiddle factors in the radix-(2 x 2) FFT algorithm. The generalization of this split vector-radix FFT algorithm to higher radices and higher dimensions is also presented. By introducing a general approach for constructing the fast Hartley transform (FHT) from the corresponding FFT, new vector- and split-vector-radix FHT algorithms having the same desirable properties as their FFT counterparts are obtained.