摘要
傅里叶变换是信号分析的最基本工具和方法之一,但其本身仍然存在较大的缺陷,例如不能提供信号在时域上的特征.短时傅里叶变换虽然可以在一定程度上弥补该缺陷,但是它的频率分辨率和时间分辨率都十分有限,只是一种折衷的解决办法.小波变换是一种快速发展和比较流行的信号分析方法,它精确地揭示了信号在时间和频率方面的分布特点,可以同时分析信号在时域和频域中的特征,并可用多种分辨率来分析信号,实现信号的有损和无损传送.文章简要地回顾了小波变换的发展历史,介绍了小波变换的基本思想、主要概念、计算方法和计算流程.最后以四个典型的实例,展示了小波变换在现代工程中的应用和它独特的优势.
Although Fourier transformation is one of the basic tools and methods in signal analysis it also has intrinsic drawbacks, such as its inability to provide the temporal or spatial characteristics of a signal. Short-time Fourier transformation has certain improvements, but users can only obtain the time- and frequency-based aspects of a signal with limited precision. Wavelet transformation is a fast-developing and popular signal analysis method. Wavelet analysis allows the use of long time intervals for more precise low-frequency information, and short regions for high-frequency information. In this paper the development of wavelet transforms is reviewed, and the funda- mental principles, concepts, calculation formulas and flowcharts are introduced. Four examples are included to il- lustrate the application of this method in modem engineering and its unique advantages in comparison to other techniques.
出处
《物理》
CAS
北大核心
2008年第1期24-32,共9页
Physics
关键词
小波变换
傅里叶变换
尺度
位移
小波簇
滤波器
wavelet transform, Fourier transform, scale, shift, wavelet, filter
