How to do inverse continuous wavelet transform from sym8 wavelet domain

I use cwt(signal,1,'sym8') to do 1-scale continuous wavelet transform to the sym8 wavelet domain. However, I didn't find the function to do the inverse continuous wavelet transform from the sym8 wavelet domain. The function icwt only applies to 'morse', 'amor', 'bump' wavelet. Anybody has an idea?

Answer 1

[Wayne King]

Hi Rubio, Why would you want to do this? The CWT should be obtained at multiple scales and those scales should be logarithmically spaced. What is your use case for obtaining the CWT of a signal at a single scale?

Why not use the MODWT? That will yield perfect inversion for a signal using the 'sym8' wavelet. Although, even if you obtain it at a single level that is not equivalent to a scale of 1.

Maybe if you describe your application a bit, I could provide a better answer.