On the structure of 2-channel paraunitary finite field multirate filter banks

Finite field multirate filter banks can be used to implement the finite field wavelet transform. The finite field wavelet transform has recently found applications in lossless image compression, error control coding and cryptography. Over the real field the polyphase form of the paraunitary multirate filter bank can be factored into lattice structures to reduce implementation complexity. Here we examine the factorisation of the paraunitary polyphase matrix over finite fields of characteristic two, i.e. (GF(2^r)), and identify further improvements when compared to a direct polyphase implementation. Implementation complexity in terms of MPUs and APUs is examined.