Introduction

In many applications of digital signal processing, it is necessary for different sampling rates to coexist within a given system. One common example is when two subsystems working at different sampling rates have to communicate and the sampling rates must be made compatible. Another case is when a wideband digital signal is decomposed into several nonoverlapping narrowband channels in order to be transmitted. In such a case, each narrowband channel may have its sampling rate decreased until its Nyquist limit is reached, thereby saving transmission bandwidth.

Here, we describe such systems which are generally referred to as multirate systems. Multirate systems are used in several applications, ranging from digital filter design to signal coding and compression, and have been increasingly present in modern digital systems.

First, we study the basic operations of decimation and interpolation, and show how arbitrary rational sampling-rate changes can be implemented with them. Then, we describe properties pertaining to the multirate systems, namely their valid inverse operations and the noble identities. With these properties introduced, the next step is to present the polyphase decompositions and the commutator models, which are key tools in multirate systems. The design of decimation and interpolation filters is also addressed. A step further is to deal with filter design techniques which use decimation and interpolation in order to achieve a prescribed set of filter specifications.