[1]虞湘宾,董涛.一种离散小波变换的快速分解和重构算法[J].东南大学学报(自然科学版),2002,32(4):564-568.[doi:10.3969/j.issn.1001-0505.2002.04.005]
 Yu Xiangbin,Dong Tao.Fast decomposition and reconstruction algorithm on discrete wavelet transform[J].Journal of Southeast University (Natural Science Edition),2002,32(4):564-568.[doi:10.3969/j.issn.1001-0505.2002.04.005]
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一种离散小波变换的快速分解和重构算法()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
32
期数:
2002年第4期
页码:
564-568
栏目:
信息与通信工程
出版日期:
2002-07-20

文章信息/Info

Title:
Fast decomposition and reconstruction algorithm on discrete wavelet transform
作者:
虞湘宾 董涛
东南大学无线电工程系, 南京 210096
Author(s):
Yu Xiangbin Dong Tao
Department of Radio Engineering, Southeast University, Nanjing 210096, China
关键词:
小波分析 快速傅里叶变换 Mallat算法 快速小波变换
Keywords:
wavelet analysis fast Fourier transform Mallat algorithm fast wavelet transform
分类号:
TN914
DOI:
10.3969/j.issn.1001-0505.2002.04.005
摘要:
通过对实序列的快速傅里叶变换算法的推导及Mallat算法原理的分析,根据离散小波变换(DWT)算法结构特征,提出了一种离散小波变换的快速分解和重构算法; 给出了相应的算法步骤.从数学理论上对该算法进行了论证,结果表明与原有的快速小波算法(Mallat算法)相比,可显著减少信号与滤波器长度N较大(大于16)时小波变换的实乘次数(分解仅为(5log2N+7)N次,重构仅为4N(1+log2N)次),提高了运算速度.且该算法有着良好的并行性,易于数字信号处理器(DSP)的快速实现.
Abstract:
On the basis of analyzing the principle of Mallat algorithm and deriving the real signal FFT algorithm, according to Discrete Wavelet Transform(DWT)structure, the paper proposes a fast decomposition and reconstruction algorithm for DWT; and the related algorithm procedures are given. The mathematical theories demonstrate that compared with conventional fast wavelet algorithm-Mallat algorithm under long signal and filter(the length N>16), the proposed algorithm can significantly reduce the real multiplication times of DWT((5log2N+7)N times only for decomposition and 4N(1+log2N)times only for reconstruction)and efficiently improve the work speed. Meantime, the algorithm is easily implemented by digital signal processing(DSP)because of its good parallel property.

参考文献/References:

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[4] 虞湘宾,毕光国.长序列信号快速相关及卷积的算法研究[J].电路与系统学报,2001,6(4):78-83.
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备注/Memo

备注/Memo:
作者简介: 虞湘宾(1971—),男,博士生.
更新日期/Last Update: 2002-07-20