图像的定点FFT变换的精度分析

A Fixed-Point FFT Precision Analysis of Image Processing

以TMS320DM642为例,针对图像处理中的定点快速傅里叶变换(FFT)进行研究分析。根据FFT的蝶形算法结构及图像数据的傅里叶变换过程,从量化误差和溢出误差的角度分析了实现图像的定点FFT过程中误差的来源,并导出了图像的FFT变换引入的误差均方值和最大噪-信比。对于2维M×N图像的FFT变换产生的量化误差的均方值与M和N成线性关系,而溢出误差的值相对于量化误差的值很小,可以忽略不记。TMS320DM642仿真器上得到的结果验证了理论分析的正确性。

The aim of this paper is to analyze the fixed-point Fast Fourier Transform （FFT） of the image based on a TI chip TMS320DM642 whose multiplier is 64 bits. By virtue of the bufferfy merging equations of the FFT and the step to achieve the Fourier Transform of the image data, the effect of noise on fixed-point FFT was discussed from two aspects ： word-length error and overflow error. The mean of the error and the max ratio of the error to signal were educed. As the M x N image for example, the analysis indicate that the word-length error mean of the fixed-point FFT is linearly increased with M and N, and the overflow error mean of the fixed-point FFT is so small compared to the word-length error mean of the fixed-point FFT that can be ignored. To test the analysis, many simulations with different M × N are conducted on DM642 EVM Block supplied by Beijing Real-time Technology CO. , LTD. The result of simulations based on ICETEK-DM642-PCI Emulator are in agreement with the theoretical analysis.