This is a survey/tutorial paper on data compression using the technique of subband coding. This is widely used in practice, for example, in the MPEG audio coder. A subband coder has two main components: a filter bank that decomposes the source into components, usually with respect to defined frequency bands; and a bank of quantizers. Without the quantizers, the subband coder-decoder is a linear periodically time-varying discrete-time system, and hence falls into the class of multirate digital signal processing systems. The paper reviews the theory of such systems, studies the perfect reconstruction problem and a variant of it, reviews subband coding theory for a stationary input signal, and describes recent work for cyclostationary signals.