有限字长对滑动窗DFT稳定性的影响研究

Research of Finite-Word-Length Effects on the Stability of the Sliding DFT

滑动窗离散傅里叶变换(DFT)具体数字实现过程中,有限字长效应引入的误差会被累积和放大,易造成系统发散和不稳定。针对该问题和现象,应用随机信号的统计特性,详细分析了信号量化噪声、旋转因子量化误差及数学运算舍入误差对滑动窗DFT稳定性的影响,并指出舍入误差所引入的直流分量是导致系统不稳定的根本原因。仿真和实验均验证了理论分析的正确性。为了解决此不稳定问题,提出两种通过交换运算次序来消除误差累积和放大的解决方案,实验和仿真结果验证了这两种方法的有效性。

The sliding discrete Fourier transform（ DFT） can experience instability issues due to the accumulation and amplification of the errors introduced by the finite-word-length effects in real practical discrete systems. In this paper,the quantization noise of A-D,the quantization error of the twiddle factors,and the rounding error of arithmetic operations are taken into consideration to analyze their influences on the stability of the sliding DFT based on the statistical properites of random signals. Based on the detailed analysis,it is revealed that the rounding error of arithmetic operations is the key reason to cause the unstable phenomenon. Both simulation and experimental results validate the theoretical analysis of instability issue of the sliding DFT. To deal with this instability problem,two methods are proposed to eliminate the error accumulation and amplification through swapping the calculation sequences of the sliding DFT. Extensive simulations and experiments are provided to verify the effectiveness of the proposed solutions.