小波变换硬件实现中有限字长效应的分析

Analysis of Finite Word Length Effect to Hardware Implementation of DWT

对小波变换硬件实现有限字长的产生和影响进行分析,并提出解决方法。对JPEG2000压缩编码标准中5/3和9/7小波变换,提出采用分数逼近小数的方法实现,比较小数系数和分数系数的变换结果,证明采用分数格式可以在有效的降低硬件实现复杂性的同时,提供相近的变换结果;通过扩大原始信号(左移若干比特)和对中间结果进行合理舍入的方法减小硬件实现中有限字长对变换精度的影响。

This paper analyzes effects of finite word length in hardware implementation of discrete wavelet transform(DWT), and puts forward the solution. Approximating the decimal fraction with fraction in lifting scheme of 5/3 and 9/7 DWT in JPEG 2000, the experiment results indicate that effect of finite word length decrease apparently. On the other hand, it reduces the effect of finite word length by enlarging the input image data (left shifting several bits) and using rounding method in DWT.