小波变换思想及其在信号处理中的应用

从傅里叶变换、短时傅里叶变换到小波变换的思想发展过程中分析了小波变换发展的必然性和重要性，并通过MATLAB仿真工具比较了三种变换在信号处理中的应用。实验结果表明，小波变换无论是对信号的时间定位还是对信号的频率定位都优于傅里叶变换和短时傅里叶变换。
关 键 词 连续小波变换; 离散小波变换; 傅里叶变换; 短时傅里叶变换

Abstract The wavelet transform has become a new signal processing technology in last decade, it has been imposed great importance by more and more theoretical workers and engineers. Simultaneity, the mathematical theory of the wavelet transform is complicated. In this paper, the basic theory and advantage of wavelet transform is simply revealed by comparing with Fourier transform and short time Fourier transform, deep cognition and understanding of wavelet transform is given by MATLAB simulation. These result shows that wavelet transform is superior to Fourier transform and short time Fourier transform both in time and frequency orientation in signal processing.
Key words continuous wavelet transform; discrete wavelet transform; Fourier transform; short time Fourier transform