What is the difference between db1, db2,db3,… in wavelet analysis?
该问题的源地址请访问Matlab Central
原文如下：
The db refers to a particular family of wavelets.
db小波是小波家族的一部分
They are technically speaking called the Daubechies extremal phase wavelets.
专业地称它们为多贝西极限相位小波
The number refers to the number of vanishing moments.
db后面那个数字代表的是消失的时刻
Basically, the higher the number of vanishing moments, the smoother the wavelet (and longer the wavelet filter).
一般来说，这个消失时刻的数字越大，这个小波越光滑（长的小波滤波器）
The length of the wavelet (and scaling) filter is two times that number, so
小波滤波器的长度（尺度）是这个数字的两倍
[LoD,HiD] = wfilters(‘db2’); %db2小波滤波器
length(LoD) %answer is 4=2*2 %结果长度为4
[LoD,HiD] = wfilters(‘db3’); %db3小波滤波器
length(LoD) %answer is 6=2*3 %结果长度为6
and so on.
诸如此类
The theoretical significance of this is that if your signal of interest is exhibiting behavior on an interval consistent with a polynomial of degree at most N and you are using a wavelet with N vanishing moments, the wavelet coefficients will be zero on that interval.
这个理论上的意义在于如果你感兴趣的信号在一个区间上是一个N阶多项式的形式，然后你使用N时刻消失的小波，这个小波系数在这个区间内将会是0
The wavelet with N vanishing moments is orthogonal to polynomials of degree at most N.
N时刻消失的小波正交于最多N阶多项式
So a ‘db1’ will return wavelet coefficients of zero on an interval if the signal is a polynomial of degree at most 1 on that interval.
因此，如果一个多项式信号的阶数最高是1的话，在一个区间上一个‘db1’小波的小波系数是0
For example:
例如
t = linspace(0,1,512);
dwtmode(‘per’);
y = t+1; % polynomial of degree 1
[C1,L1] = wavedec(y,2,’db1’);
d1 = detcoef(C1,L1,1);
plot(d1) %detail coefficients are all approximately zero
y1 = t.^2+1; % polynomial of degree 2
[C2,L2] = wavedec(y1,2,’db1’);
d1 = detcoef(C2,L2,1);
plot(d1) % detail coefficients are not all zero