一种快速离散小波变换算法及其在语音信号中的应用.pdfVIP

Computer Engineering and Applications 计算机工程与应用 2011 ，47 （35） 143 一种快速离散小波变换算法及其在语音信号中的应用 徐伟业 XU Weiye 南京工程学院 通信工程学院，南京 211016 College of Communications Engineering ，Nanjing Institute of Technology ，Nanjing 211016 ，China XU Weiye.Fast discrete wavelet transform and its application to speech signal processing.Computer Engineering and Applications ，2011 ，47 （35 ）：143-146. Abstract ：With the research standard of wavelet analysis improving ，the application field of the wavelet transform is keep- ing 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 af- fected.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 struc- ture 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. Key words ：Fast Fourier Transform （FFT ）；fast discrete wavelet transform ；multi-resolution analysis ；decomposition and recon- struction ；speech signal processing 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。 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 DOI ：10.3778/j.issn. 1002-8331.2011.35.040 文章编号：1002-8331（2011 ）35-0143-04 文献标识码：A 中图分类号：TN