We present a new approach to the analysis of square-wave voltammetry in the frequency domain. By extending our earlier work (J. Electroanal. Chem. 480 (2000) 133) on the numerical simulation of ac sine wave voltammetry, we are able to solve the governing equations when a square waveform of any amplitude is superimposed onto a linearly varying dc potential which is swept at a finite scan rate. By considering the numerical results in the frequency domain by using the fast Fourier transform (FFT) method, we are able to develop a very simple and general form of analysis which will theoretically allow consideration of reaction phenomena over a very wide range of timescales using a single potential sweep. We go on to develop some novel theoretical analyses, which support our numerical results, using an assumption that the applied square-wave signal is superimposed on top of a fixed (or very slowly varying) dc signal. This allows us to give exact and surprisingly simple analytical results relating the amplitude and phase of the output signal at the half-wave potential (at odd multiples of the fundamental frequency), to the amplitude of the applied square-wave signal, for any amplitude of the applied signal. Finally, we give brief experimental results showing qualitative agreement with our simulation results.