Delsarte theory for subsets of commutative association schemes gives a relationship between codes and designs in terms of spherical Fourier transforms. In this talk, we apply the idea of Delsarte theory for quotients of commutative association schemes. Then we have a relationship between the geometry of fibers and the harmonic analysis on quotients of association schemes. In particular, by considering a regular tree as an infinite commutative association scheme, we have a relationship between the girth and the eigenvalues of finite regular graphs, which was proved by H. Nozaki [Graphs and Combinatorics (2015)]. We also discuss that Ihara's fomura for zeta functions on finite regular graphs can be understand by our Delsarte theory. A part of this talk is joint work with Masato Mimura (Tohoku University) and Hiroshi Nozaki (Aichi University of Education).