A Grouped Fast Fourier Transform Algorithm Design For Selective Transformed Outputs

In this paper, the grouped scheme is specially applied to compute the fast Fourier transform (FFT) when the portions of transformed outputs are calculated selectively. The grouped FFT algorithm applies the scheme of the grouped frequency indices to accelerate the computation of selected DFT outputs. The advantage of the grouped FFT algorithm is that it is more cost-effective than the convenient FFT algorithms when the authors need to compute parts of the transformed outputs, not all outputs. For computing all transformed outputs of the DFT, the computational complexity of the proposed FFT method is less than that of the radix-2 method. Meanwhile, the computational complexity of the proposed fast method approximates to that of the radix-4 FFT algorithm. By sharing coefficients of the twiddle factors in the same frequency group, the grouped FFT can be implemented with hardware sharing VLSI architectures