1) ability to reinject a previously captured waveform (like a general waveform generator)
2) ability to display the Z-transformtion of a signal
special 3) operations on FFTs and Z-transformtions and inject waveforms resynthesized out of FFTs and Z-transforms into the circuit 
1) Unfortunately, the scope is only a scope, not a signal generator.
2) The Z-tranform of a signal is nothing more than the sum of the 1st sample multiplied by 1, the 2nd by z^-1, the 3rd by z^-2,..., so I wonder how you could display such a thing
3) Applying a user defined filtering to the captured waveform would be a good feature
I hope Shafri tool for the Rigol gives the possibility to export captured waveforms into an easy readable format (e.g. csv), which could then be imported into Matlab, Excel or other tools. I don't see this option into Ultrascope.
If this feature is supported, algorithms would become easily to develop and test outside, and then put into the application, not leaving Shafri alone in this work

ok, i need to study basic first! Fourier Trasform... have been reading for hours (in wiki, book) it seems everytime i dig more into the detail, there is a new hole (aspect) to dig. esp this discrete stuffs, windowing (blackman hann etc). this highly mathematical stuff drives me crazy! i thought i can finish it at 12pm, but now its 3am already, and i havent got anything!... arghh! tomorrows working! 
I think they usually explain these things in a bad way for an engineer (using math only, rather than math and examples), while the core of the thing is quite simple (for example like I told above for the Z-transform). Don't give up, and if you need it, just ask, someone will find the right way to explain.