傅里叶变换是用一系列不同频率的正余弦函数去分解原函数，变换后得到是原函数在正余弦不同频率下的系数。



小波变换使用一系列的不同尺度的小波去分解原函数，变换后得到的是原函数在不同尺度小波下的系数。



不同的小波通过平移与尺度变换分解，平移是为了得到原函数的时间特性，尺度变换是为了得到原函数的频率特性。



小波变换步骤：



1.把小波w(t)和原函数f(t)的开始部分进行比较，计算系数C。系数C表示该部分函数与小波的相似程度。



2.把小波向右移k单位，得到小波w(t-k)，重复1。重复该部知道函数f结束.



3.扩展小波w(t)，得到小波w(t/2)，重复步骤1,2.



4.不断扩展小波，重复1,2,3.

我这里使用的haar小波，缩放函数是[1 1]，小波函数是[1 -1]。-Fourier transform is a series of sine and cosine functions of different frequencies to the decomposition of the original function, after transform the original function in different frequency sine and cosine coefficients. Wavelet transform using a range of different scales of the wavelet decomposition to the original function, after transform the original function coefficients at different scales wavelets. Different wavelet decomposition by translation and scaling, translation is to get the time characteristics of the original function, in order to obtain the frequency scaling characteristics of the original function. Wavelet transform steps: 1. wavelet w (t) and the original function f (t) of the beginning of the comparison, calculate the coefficient C. The coefficient C indicates the degree of similarity of the function and wavelets. 2. Wavelet k units to the right, get the wavelet w (tk), repeat 1. Repeat this end portion know the function f. 3. Extended wavelet w (t), to obtain the