| 引用本文: | 蒋增荣,成礼智.二维离散余弦变换与二维离散Fourier变换的快速算法.[J].国防科技大学学报,1992,14(1):69-75.[点击复制] |
| Jiang Zengrong,Cheng Lizhi.Fast Algorithm for Two-dimensional Discrete Cosine Transform and Two-dimensional Discrete Fourier Transform[J].Journal of National University of Defense Technology,1992,14(1):69-75[点击复制] |
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| 二维离散余弦变换与二维离散Fourier变换的快速算法 |
| 蒋增荣, 成礼智 |
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(系统工程与应用数学系)
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| 摘要: |
| 文中提出 N×M2D-DCT(Ⅱ)的一种快速算法，其需实运算量为: Mu=1/2NMlog2N+1/4MNlog2M,Ad=3/2NM log2NM-3MN-1/2M2+M+N（其中N、M为2的幂)。当 N=M 时，与文[5]的结果一样。这是目前最好的结果。但文[5]算法不稳定，容易产生较大的误差。本文克服了这一缺点。并利用此 2D-FCT (Ⅱ)导出了2D-DCT. 2D-DST 和 2D-DCST 的快速算法及 2D-DFT的一种快速算法。2D-DFT快速算法的运算量与文[l]中用 FPT 计算 2D-DFT相近。 |
| 关键词: 快速算法，离散余弦变换，离散富里叶变换 |
| DOI： |
| 投稿日期：1991-02-02 |
| 基金项目: |
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| Fast Algorithm for Two-dimensional Discrete Cosine Transform and Two-dimensional Discrete Fourier Transform |
| Jiang Zengrong, Cheng Lizhi |
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(Department of System Engineering and App1ied Mathematics)
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| Abstract: |
| A fast a1gorithm for computing N×M 2D-DCT(Ⅱ) is deve1oped. The amount of the real operations are:Mu=1/2NMlog2N+1/4MNlog2M,Ad=3/2NMlog2NM-3MN-1/2M2+M+N,where N=2t,M=2r.When N=M,the result is the same as in [5],which is the best result at present. But the algorithm in [5] has instability leading to large errors easily.This limitation has been overcome in the paper. We also derive some algorithms about 2D-DCT,2D-DST,2D-DCST. A fast algorithm about 2D-DFT is developed in particular,the amount of the operations in paper is similar to that in [1] with FPT to calculate 2D-DFT. |
| Keywords: fast algorithm,discrete cosine transform,discrete Fourier transform |
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