  I discuss some problems featuring scattering due to discrete edges on certain
structures. These problems stem from linear difference equations and the
underlying basic issue can be mapped to Wiener-Hopf factorization on an annulus
in the complex plane. In most of these problems, the relevant factorization
involves a scalar function, while in some cases a nxn matrix kernel, with n>=2,
appears. For the latter, I give examples of two non-trivial cases where it can
be further reduced to a scalar problem but in general this is not the case.
Some of the problems that I have presented in this paper can be also
interpreted as discrete analogues of well-known scattering problems, notably a
few of which are still open, in Wiener-Hopf factorization on an infinite strip
in complex plane.
