signal analysis - infomation about Stockwell Transform

I need some information about Stockwell transform (also known as the S-transform):

1. How can I implement it in MATLAB?


2. *Does it give you the damping ratio $\zeta$ of a signal like the complex Morlet continuous wavelet? $$x(t)= e^{-\omega_{n}\zeta}\sin(\omega_{d}t+\theta )$$


3. What are its advantages compared to CWT?

The S-transform defined as follows:

$$s( \tau ,f)= \int_{-\infty}^\infty h(t) \frac{\ |f|}{\ \sqrt{2 \pi } } e^{ \frac{-(t- \tau )^{2} f^{2}}{2} } e^{-j 2 \pi f} dt$$ (This is a good tutorial about the S-Transform)

These are the first few question that I can think about at the moment. It seems no one asked about the S-transform before, so put your questions in this post by editing it, and answer them if you know them. Someone with enough reputation put a tag for S-transform please. Thanks a lot.