  Bloch wave homogenization is a spectral method for obtaining effective
coefficients for periodically heterogeneous media. This method hinges on the
direct integral decomposition of periodic operators, which is not available in
a suitable form for almost periodic operators. In particular, the notion of
Bloch eigenvalues and eigenvectors does not exist for almost periodic
operators. However, we are able to recover the homogenization result in this
case, by employing a sequence of periodic approximations to almost periodic
operators. We also establish a rate of convergence for approximations of
homogenized tensors for a class of almost periodic media. The results are
supported by a numerical study.
