Let G be a connected locally finite graph. A matrix \(D=(d_{ij})\) is a front divisor of G if there is a partition of V(G) into classes \(V_ 1,V_ 2,V_ 3,..\). such that (1) for each i, j and each \(v\in V_ i\) there are exactly \(d_{ij}\) edges emanating from v and having the terminal vertex in \(V_ j\), and (2) for each i, the set \(V_ i\) is finite. Let \(D^{\sim}\) be the matrix determined by \((D^{\sim})_{ij}:=(d_{ij}d_{ji})^{1/2}\). If X is a graph or a matrix, let \(\sigma\) (X) denote its spectrum. It is shown that \(\sigma (D^{\sim})\subseteq \sigma (G)\). If G is a distance-regular graph, then the distance partition of G determines a front divisor P. It is shown that in this case \(\sigma (P^{\sim})=\sigma (G)\). As an application, the spectra of all infinite locally finite distance-regular graphs are determined.