调制FFT及其在离散频谱校正技术中的应用

提出了一种调制快速傅立叶变换(FFT),通过时域调制对实信号进行移频,打破频域内的对称性,再进行传统的FFT.该算法克服了直接进行FFT计算结果有一半冗余的缺点.将频率分辨率提高了一倍.提高了频率定位的精确度,从而减小了最大的幅值和相位误差,并进一步提高了抗噪性能.以比值校正法和相位差法为例,将调制FFT应用到离散频谱校正技术中,解决了基于FFT的离散频谱校正方法由于噪声影响而出现的一些问题,进一步提高了校正精度和抗噪性能.理论分析和Monte Carlo计算机模拟实验验证了上述结论的正确性.

Modulated FFT and its application in the discrete spectrum correction

In view of half of the calculation results are redundant during traditional Fast Fourier transform (FFT), a novel algorithm based on modulated FFT of real signals is proposed to solve the problem. The algorithm shifts frequency of real signals by time domain modulation before turning to the traditional FFT, which breaks the symmetry of frequency domain. Thus, the frequency resolution can be double increased and the accuracy of frequency positioning and anti-noise performance can be improved as well. In this paper, Ratio Correction and Phase Difference Correction on discrete spectrum are taken as examples, in which the Modulated FFT has been applied to discrete spectrum correction technology. It can solve the problems due to the influence of noise, by applying discrete spectrum correction methods based on FFT. And the correction accuracy and anti-noise performance can be further improved. Both theoretical analysis and Monte Carlo computer simulation method prove that the proposed algorithm is correct and effective.