小波分解与重建中产生频率混淆的原因与消除算法
|
摘要
Mallat算法，即基于多分辨分析的金字塔算法是小波变换的快速算法，在工程上获得了广泛的应用但是作者发现，Mallat算法存在频率混淆．本文全面深入地分析了Mallat算法存在频率混淆的原因，是由正交镜象滤波器（QMF）的频域特性、隔点采样和隔点插零造成的．进而提出了一种改进的小波分解与重建算法，即结合FFT的小波变换算法该算法完全消除了频率混淆.
Mallat algorithm, which is also called the pyramid algorithm based on multiresolution analysis, is the fast algorithm of wavelet transform. It is used widely in engineering. The authors found that There erists frequency aliasing in Mallat algorithm. Sometimes it is severe. The reasons of the frequency aliasing in Mallat algorithm are analyzed profoundiy in this paper. It is caused by the frequency charater of the quadriture mirror filters and the process of keeping one sample out of two and the process of putting one zero between each sample in Mallat algorithm. This paper presents an improved algorithm . Which is called an algcrighm based on wavelet transform and FFT. It is shown that Using this algorithm the frequency aliasing is avoided.
Mallat algorithm, which is also called the pyramid algorithm based on multiresolution analysis, is the fast algorithm of wavelet transform. It is used widely in engineering. The authors found that There erists frequency aliasing in Mallat algorithm. Sometimes it is severe. The reasons of the frequency aliasing in Mallat algorithm are analyzed profoundiy in this paper. It is caused by the frequency charater of the quadriture mirror filters and the process of keeping one sample out of two and the process of putting one zero between each sample in Mallat algorithm. This paper presents an improved algorithm . Which is called an algcrighm based on wavelet transform and FFT. It is shown that Using this algorithm the frequency aliasing is avoided.
引文
1Mallat S G. A Theory for Multiresolution Signal Decomposi-tion: Wavelet Representation.IEEE Transactions on PattemAnalysis nad Machine Intelligence,1989.11(7): 674 ~ 693
2 Ya Wu, DU R. Feature Extraction and Assessment UsingWavelet Packets For Monitoring of Machining Processes. Me-chanical Systems and Signal Processing, 1996,10(1):29 ~ 53
3 Ingrid Daubechies.Orthonormal Bases of Compactly Supported Wavelets. Communications on Pure and Applied Mathematics,1988,XLI,909~996
4秦前清,杨宗凯.实用小波分析,西安:西安电子科技大学出版社,1995.29~53
5刘维国,杨兆进,郭惠娟等.小波变换及其在地震资料处理中的应用.哈尔滨工业大学学报,1995,27(1):1~4
6张东来,许殿国,王炎.B-小波的特点及其在钢丝绳断丝信号处理中的应用.哈尔滨工业大学学报,1998,30(4):107~112
2 Ya Wu, DU R. Feature Extraction and Assessment UsingWavelet Packets For Monitoring of Machining Processes. Me-chanical Systems and Signal Processing, 1996,10(1):29 ~ 53
3 Ingrid Daubechies.Orthonormal Bases of Compactly Supported Wavelets. Communications on Pure and Applied Mathematics,1988,XLI,909~996
4秦前清,杨宗凯.实用小波分析,西安:西安电子科技大学出版社,1995.29~53
5刘维国,杨兆进,郭惠娟等.小波变换及其在地震资料处理中的应用.哈尔滨工业大学学报,1995,27(1):1~4
6张东来,许殿国,王炎.B-小波的特点及其在钢丝绳断丝信号处理中的应用.哈尔滨工业大学学报,1998,30(4):107~112
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心