定点FFT的有限字长效应分析

Analysis of Finite Register Length Effects Based on TMS320C62x

目的 以TMS320C62x为例,针对定点快速傅里叶变换(FFT)进行研究方法借助复平面单位圆,对采用原码截断算法的字长误差进行理论分析,对原码、补码格式下截断与舍入算法进行仿真比较;并讨论噪声对字长误差的影响结果 对线性相位信号作r级FFT运算时,原码截断算法产生的有限字长误差会使频域输出绝对值减小,其误差均值和方差都与r成线性关系;对信号加入适当的白噪声。

Aim To analyze the finite register length effects based on TMS320C62x whose multiplier is 16 bit. Methods The word length error using truncation of sign magnitude code was analyzed on the unit circle of complex plane. The computer simulations using truncation and rounding of sing magnitude code and complementary code were given. The effect of noise on finite register length error was discussed.Results When using linear phase signal and algorithm of truncation of sign magnitude code, the absolute values of output in frequency domain decrease because of the word length error of r steps' FFT. The error's mean and variance are both linearly increased with r . The mean of errors can be decreased by adding the white noise to the signal. Conclusion The result of simulations based on TMS320C62x's simulator are in agreement with the theoretical analysis.