I figured out that I've implemented a real-time wavelet transform while I was doing this... :) I tried and couldn't find any good apps that would use it to display real-time analysis of sound, so I made one. Actually, I was working on the AI to generate music, but I haven't got to the AI bit yet, and decided to release this quickly, just for fun, see what people think. I think much better visualisations can be made from the output of this algo...
I guess you're missing the detail of how it's actually implemented in practice. The short description would be just "wavelet transform" I guess. The details is in how to implement it efficiently so that it can run on the phone in real-time, and draw the visualisation at the same time, without drowning the CPU (plus the additional feature of high-precision detection, which is not solved by wavelet transform itself). I will describe it in more details when I'll be open sourcing the algorithm (after I've implemented something on top of it that I could potentially start selling).
That would be hard to target different phones... I am just using SSE/AVX (via Apple's Accelerate framework) for now for some parallelisation, helps to speed up the detection x10.