基于连续小波理论的时间尺度变换实现

Implementation of Time\|Scale Transformation Based on Continuous Wavelet Theory

时间尺度变换就是使信号在时域上压缩或扩展而幅度不发生变化。推导了基于连续小波变换的函数时间尺度变换公式 ,在已知任意平方可积函数 f( t)的条件下 ,通过连续小波变换和反变换求得期望的 g( t) =f( t/λ)。在小波变换条件下 ,函数的时间尺度变换可以通过等量代换进而转化小波滤波器的时间尺度调制来获得 。

The basic objective of time\|scale transformation is to compress or expand the signal in time field while keeping the same spectral properties.This paper derives time\|scale transformation formula based on continuous wavelet transform.Under the condition of any given square\|integrable function f(t),g(t)=f(t/λ) is derived by continuous wavelet transform and its inverse transform.The result shows that the time\|scale transformation may be obtained through the modification of the time\|scale of wavelet function filter using equivalent substitution.The paper demonstrates the result by theory derivations and experimental simulation.