Smooth wavelets, transform coding, and Markov-1 processes

This paper compares the energy compacting properties of unitary transforms from transform coders and two-band paraunitary filter banks from subband coders using a cost criterion that is proposed. Stationary processes for which paraunitary filters have better energy compaction than unitary filters are denoted as subband optimal, and all subband optimal processes are analytically characterized for the case of length-4 filters. It is shown analytically for length-4 filters and empirically for longer-length filters that Markov-1 processes are subband optimal and that the Daubechies (1988) maximally smooth wavelet sequences achieve better energy compaction than the best unitary filters for Markov-1 inputs.