基于VC的补零DFT在图像处理中的应用

The Application of Zero Padding of the DFT in Digital Image Processing Based on VC

由Cooley和Tukey提出的快速傅里叶变换算法(Fast Fourier Transform,FFT)是针对数据长度N等于2的整数次幂的算法,也即基2的FFT算法。而在实际数字图像处理应用中,图像的宽和高不可能都是2的整数次幂,解决这一矛盾的一种有效的方法就是在图像数据后补零,使其长度达到2的整数次幂。本文对FFT的补零问题进行了分析,并基于VC++的图像处理程序设计,对解决二维图像处理中数据长度不等于2的整数次幂的FFT算法问题进行了探索和应用研究。

The Fast Fourier Transform （FFT）, developed originally by Cooley and Tukey , is one of the Discrete Fourier Transform （DFT） algorithms . The algorithm, which suffers from the significant limitation of only working for sequence lengths that are an integral power of 2, is called radix-2 FFT. When the image data to be transformed is not an integral power of 2, it is still possible to use the radix-2 algorithm. One of the possibilities is that we ‘zero pad＇ the sequence （the row or the column of the image data） until it fits the next nearest integral power of 2, i.e. we extend the length by appending zeros onto the end of the sequence. An example is given in this text based on Visual C＋＋.