I don't see how that would help: e^(i*√s) is only further analyzable when s is the square of a rational number, but even then it won't help you go further: e^i*k is not rational (k≠0). In something like DFT or FIR analysis, it wouldn't help to work with spread instead of angle, I think. Integrating over s^2 only adds more steps, and I also don't see how it could help numerical approximation.