Multirate signal processing on finite fields

The paper addresses the problem of multirate signal processing over arbitrary fields. Studies of multirate systems and filter banks have proceeded in parallel, and a wealth of results are available in literature. The authors concentrate their attention on cyclic systems. These structures are ideally suited to generalising the concepts to finite fields. The perfect reconstruction property for quadrature mirror filter banks is obtained. It is shown how the cyclic wavelet transform (CWT) can be derived from such systems; the relationships between cyclic filter banks and CWTs are explored in detail. The results obtained are potentially very well suited for speech and image encoding, as well as for fast algorithms in signal processing.