摘要
随着小波分析的理论研究水平不断提高,其应用领域也在不断扩展。特别是其多分辨率分析和Mallat算法在数字信号处理和数字通信中得到了广泛的应用。但是如果直接按照上述算法计算信号的小波分解和重构,其计算量将是很大的。通过对实序列的快速傅里叶变换(FFT)算法的推导及Mallat算法原理的分析,根据离散小波变换算法结构特征,提出了一种基于FFT的快速离散小波变换算法,并从数学理论上进行了论证。同时把该算法应用到实际的语音信号处理中,得到了很好的快速分解和重构效果。
With the research standard of wavelet analysis improving,the application field of the wavelet transform is keeping spreading.Especially it is widely used in digital signal processing and digital communication because of its multi-resolu- tion analysis and Mallat algorithm.However, if the signal decomposition and reconstruction is calculated based on the above-mentioned algorithm, the computational complexity will be very large, and the timely processing of signal will be affected.On the basis of analyzing the principle of Mallat algorithm principle,by deriving the real signal Fast Fourier Transform （FFT） algorithm,a fast wavelet transform algorithm based on FFT is proposed in terms of discrete wavelet transform structure in this paper.This algorithm is testified well from mathematical theory.Meanwhile, the proposed fast algorithm is applied to the speech signal processing,and fast decomposition and reconstruction result is obtained well.
出处
《计算机工程与应用》
CSCD
北大核心
2011年第35期143-146,149,共5页
Computer Engineering and Applications
基金
南京工程学院科研基金项目(No.QKJB2009019)
关键词
快速傅里叶变换
快速离散小波变换
多分辨率分析
信号分解和重构
语音信号处理
Fast Fourier Transform（FFT）
fast discrete wavelet transform
multi-resolution analysis
decomposition and reconstruction
speech signal processing
