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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 .
Discrete Cosine Transform (DCT) is an important mathematical tool in many fields such as digital image processing.This paper calculates the DCT by a new Fourier analysis technique called Arithmetic Fourier Transform (AFT) .In this paper, the AFT of the even function is improved. The AFT algorithm not only reduces the number of sample points required for AFT in half, thus reducing the amount of calculation required for addition by half, but more importantly it establishes a direct relationship between AFT and DCT, thus providing an AFT algorithm suitable for calculating DCT In this paper, the algorithm of calculating DCT with improved AFT is deduced and the algorithm is analyzed briefly.The multiplication of this algorithm is only O (N), and it has the characteristics of consistent formula, simple structure, easy parallelism and suitable for VLSI design , Has opened up a new way for the rapid calculation of DCT.