连续小波变换与几种具体信号的傅立叶变换的比较

列出门函数、单边指数函数和阶跃函数这三种具体信号的连续小波变换与傅里叶变换的表达式，并通过表达式对连续小波变换与傅里叶变换进行比较．结果表明：傅里叶变换是线性变换，具有统一性和相似性，但不具有局部化性质，不能作局部分析；小波变换也是线性变换，同样具有统一性和相似性，并且是稳定的，还具有时一频同时局部性和自适应性．由此说明了小波变换在分析和处理信号时比傅里叶变换更加灵活、更加全面和深入．

Comparison of Fourier Transforms and Continuous Wavelet Transforms on Three Concrete Signals

In the paper, Fourier transform is compared to continuous wavelet transform through listing the expressions of continuous wavelet and Fourier transforms on gate function , unilateral exponential function and step function concrete signals, The result shows that, Fourier transform is a kind of linear transform, which has unity and similarity, but doesn＇ t have local property, and can＇ t be used in local analysis; continuous wavelet transform is a type of linear transform which has unity and similarity too, and also has time - frequency local property and adaptivity. So the wavelet transform is more flexible and comprehensive than Fourier transform in analyzing and dealing with signals .