Abstract: It expands transform nuclear of one dimensional Discrete Cosine Transform(DCT) into the two dimensional fractional type, gets two dimensional discrete fractional cosine transform of Pei type. Then an improved type of two dimensional discrete fractional cosine transform is purposed which is a weighted combination of the integer-order cosine transforms of the original signal. It analyzes the period connection of the two types transformations based on feature value and feature vector of DCT. Numerical value simulation result indicates that the two types of transformation can get the same results, and it can be applied in image processing, digital watermark technology.

Key words: Fourier Transform(FT), Discrete Cosine Transform(DCT), feature vector, two dimensional space

摘要： 将一维离散余弦变换的变换核扩展到二维分数形式，得到Pei形式的二维离散分数余弦变换。通过整数阶余弦变换的线性叠加构造一种改进形式的二维离散分数余弦变换，并基于特征值和特征向量理论，分析2种离散分数余弦变换的周期关系。数值仿真结果表明，2种形式可以达到相同的变换结果，适用于图像编码、数字水印等领域。

关键词: 傅里叶变换, 离散余弦变换, 特征向量, 二维空间

CLC Number: 

• TN911