使用CWT完美重构小波变换
perfect reconstruction of wavelet transform using CWT
如果我执行标准小波变换然后执行逆变换，我希望得到原始信号：
% dummy series:
Fs = 1e3;
t = 0:1/Fs:1;
x = exp(cos(2*pi*32*t).*(t>=0.1 & t<0.3) + sin(2*pi*64*t).*(t>0.7));
% perform default transform and inverse
wt=cwt(x)
rx=icwt(wt)
% plot
plot(t,x,t,rx)
除了偏移之外，平坦周期信号失真。
似乎可以执行 transform/inverse 并具有接近身份功能的东西，如此处 wavelet reconstruction of time series R ，但阅读 cwt 的 tutorials/help 我不知道如何实现这一点。
The matlab documentation explains that the CWT is not the best choice for perfect reconstruction. However if you want to compare different bands as signals with the same size as the original, you can use the MODWT (or the shift-invariant DWT by cycle-spinning，有时被称为有洞）。
如果我执行标准小波变换然后执行逆变换，我希望得到原始信号：
% dummy series:
Fs = 1e3;
t = 0:1/Fs:1;
x = exp(cos(2*pi*32*t).*(t>=0.1 & t<0.3) + sin(2*pi*64*t).*(t>0.7));
% perform default transform and inverse
wt=cwt(x)
rx=icwt(wt)
% plot
plot(t,x,t,rx)
除了偏移之外，平坦周期信号失真。
The matlab documentation explains that the CWT is not the best choice for perfect reconstruction. However if you want to compare different bands as signals with the same size as the original, you can use the MODWT (or the shift-invariant DWT by cycle-spinning，有时被称为有洞）。