If one takes a cyclic group and a function on this group, and performs harmonic analysis on it (classical Fourier analysis), the result is a set of coefficients, each one of them corresponding to frequencies, ie intuitively particular paths in the cyclic Cayley graphs (in this case, loops with step 1, 2, etc...)
Is this the same for more general groups (dihedral, alternating, symmetric, etc..) ? Does n-dimensional coefficients (or individual elements of these matrices) corresponds to particular paths in a corresponding Cayley graph of the group ?
Thanks