I know wavelets were all the rage a few years ago, but I missed that boat and am wondering if it is worth putting significant effort into learning about them. My impression is that they were a little bit of a fad, and now have more limited applications than first assumed (similar to compressed sensing).*
My (very limited) understanding is that the wavelet transform is similar to the Fourier transform, except the filter bank/basis function set can be many other things besides complex exponentials (as in the DFT). I suppose that would make the short time Fourier transform a subset of the wavelet transforms.
So I have two questions:
- Is my understanding basically correct? If not, can anyone point me to any good tutorials?
- What are the main practical applications of wavelet transforms? The main thing I'm aware of is image compression.
Thanks for any pointers!
*Lest any wavelet or compressed sensing aficionados get up in arms, I know both have useful applications. But unsurprisingly neither has turned out to be the silver bullet some initially thought they might be. There are truly very few seminal breakthroughs.
To hopefully clarify the second question a bit, I'm interested in classes of DSP problems where wavelets are significantly superior to other methods in general. As an analogy, deep learning is obviously strong on image classification when you have a large and broad set of training data.