  We obtain a canonical form of a quadratic Hamiltonian for linear waves in a
weakly inhomogeneous medium. This is achieved by using the WKB representation
of wave packets. The canonical form of the Hamiltonian is obtained via the
series of canonical Bogolyubov-type and near-identical transformations. Various
examples of the application illustrating the main features of our approach are
presented. The knowledge of the Hamiltonian structure for linear wave systems
provides a basis for developing a theory of weakly nonlinear random waves in
inhomogeneous media generalizing the theory of homogeneous wave turbulence.
