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

Abstract: 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-resolution 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.

Key words: Fast Fourier Transform（FFT）, fast discrete wavelet transform, multi-resolution analysis, decomposition and reconstruction, speech signal processing