Training a network to learn a set of periodic input/output sequences effectively makes the network learn a mapping between amplitudes and phases in Fourier space. The spectral backpropagation (SBP) training algorithm is a different way of doing this task. It measures the Fourier series components of the output error sequences and minimizes the total spectral energy as an adaptation criterion. This approach can train not only the weights but also time delays associated with the interconnects. Furthermore, the cells can have finite bandwidth via a first-order low-pass filter. Having adaptable time delays gives the SBP algorithm a powerful way to control the phase characteristics of the network.