An Efficient Algorithm of 10-Point DFT and its Applications

An efficient algorithm for computing 10-point DFT, which can contribute fast algorithms to more N-point DFTs, is developed. The computation of one 10-point DFT requires only 20 real multiplications, 84 real additions and 4 real right-shiftings 2 bits. According to the principles of decimation-in-time (DIT) or decimation-in-frequency (DIF) or double factors algorithm and the efficient algorithm of 10-point DFT, 10^M, 10×M, 2^M×10, 4^M×10-point DFT have their own efficient algorithms, respectively. Thus, many N-point DFTs are possessed of own fast fourier transform algorithms. Especially, in efficient algorithm for computing 10-point DFT, in other words, in radix-10 FFT algorithm, one 10²-point DFT requires 720 real multiplications, 1840 real additions and 80 real right-shiftings, one 10³-point DFT requires 12760 real multiplications, 28580 real additions and 1200 real right-shiftings 2 bits, and one 10⁴-point DFT requires 183560 real multiplications, 387780 real additions and 16000 real right-shiftings 2 bits.