离散余弦变换的改进的算术傅立叶变换算法

离散余弦变换(DCT)是数字图像处理等许多领域的重要数学工具.本文通过一种新的傅立叶分析技术——算术傅立叶变换(AFT)来计算DCT.本文对偶函数的AFT进行了改进.改进的AFT算法不但把AFT所需样本点数减少了一半,从而使所需加法计算量减少了一半,更重要的是它建立起AFT和DCT的直接联系,因而提供了适合用于计算DCT的AFT算法.本文推导了用改进的AFT计算DCT的算法并对算法进行了简要的分析.这种算法的乘法量仅为O(N),并且具有公式一致,结构简单,易于并行,适合VLSI设计等特点,为DCT的快速计算开辟了新的途径.

An Algorithm for Computing DCT Using Improved Arithmetic Fourier Transform

The discrete cosine transform (DCT) is an important mathematical tool in digital image processing and many other fields.In this paper,a new Fourier analysis technique called the arithmetic Fourier transform (AFT) is used to compute DCT.The AFT of even functions is improved in this paper.The improved AFT reduces the samples needed to a half,consequently reduces the additions needed to a half.More importantly,it builds up a direct relationship between AFT and DCT.The algorithm for computing DCT using improved AFT is then deduced.This algorithm has many good performances such as it needs few multiplications ( O(N) ),it has a unified formula and a simple structure,it can be easily performed in parallel and it is especially suitable for VLSI designing.The algorithm creates a new approach to the fast computation of DCT.