Novel recursive discrete Fourier transform with compact architecture

We propose the novel recursive method to compute discrete Fourier transforms (DFT). The advantages of proposed recursive structure are the reduction of the loop computing numbers and the signal to quantization noise ratio (SQNR) is greater than the well-known Goertzel´s method. The compact recursive DFT applies the grouped frequency indices to accelerate the computation of the DFT transformation. By sharing the loop and output coefficients, we can implement the recursive DFT with hardware sharing architectures.