Summary: Wavelet transforms for discrete-time periodic signals are developed. In this finite-dimensional context, key ideas from the continuous-time papers of Daubechies and of Cohen, Daubechies and Feauveau are isolated to give a concise, rigorous derivation of the discrete-time periodic analogs of orthonormal and symmetric biorthogonal bases of compactly supported wavelets. These discrete-time periodic wavelets are expressed in terms of circular FIR filters, and thus lead to fast wavelet transforms whose complexity is of order \(N\).