## Abstract

Multirate transformations, better known as *multirate systems*, operate on discrete signals that have different rates. A single discrete transformation (tf) is characterized by two rates, the input and the output rate, but in a combination of tfs we may find several rates. Typical components of multirate tfs belong to the class of QIL tfs, which include up-samplers, down-samplers, interpolators, decimators and fractional interpolators. Sometimes, exponential modulators, which belong to the broader class of PIL tfs, are considered. The peculiarity of multirate tfs lies in certain properties which allow several alternative architectures with interesting consequences for applications. In this chapter, multirate systems are developed in the *signal-domain*, where the Unified Signal Theory is particularly useful for the relevance it gives to the domains and consequently to the *rates*. The signal-domain approach is atypical in the literature where the *z-domain-approach* is commonly used. Another difference with the literature is in multidimensional multirate systems where we use a *representation-independent* formulation of lattice operations, whereas other authors make use of heavy matrix manipulations.

## Keywords

Orthogonal Frequency Division Multiplex Impulse Response Finite Group Orthogonal Frequency Division Multiplex System Parallel Architecture## References

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