Conclusions

I have shown that the minimum-phase helical factorization of the Helmholtz equation can be applied recursively to extrapolate waves up to 90$^\circ$, demonstrating the power of helical boundary conditions to solve wave-equation PDE's. For the constant coefficient case, however, pure Fourier domain methods are still more efficient than the helical factorization, and do not suffer from the technical problems related to the factoring of functions with roots near the unit circle. This means that the methodology in this chapter does not have wide practical value, but rather serves as an conceptual introduction to the following chapters.