EVOLUTION OF LOCAL SPECTRA IN SMOOTHLY VARYING NONHOMOGENEOUS ENVIRONMENTS - LOCAL CANONIZATION AND MARCHING ALGORITHMS

By applying the windowed Fourier transform directly to the Helmholtz w ave equation a new formulation that governs the evolution of the local spectra of wave fields in a general nonhomogeneous environment is der ived. By further invoking the so-called locally homogeneous approximat ion, a simplified evolution equation, termed as the locally homogeneou s wave equation is developed, together with an upper bound on the erro r associated with the approximation. It is shown how simple analytical solutions of the new wave equation in a general smoothly varying nonh omogeneous environment can be obtained using well-known analytical tec hniques, and how the marching methodology connects these new solutions to the original problem described by the Helmholtz equation.