Properties of optimal, compaction filters in subband coding

Optimum compaction filters find application in the design of orthonormal subband coders with maximum coding gain. The compaction gain for a process is defined, and a number of its properties studied. Bounds on the compaction gain are established, and the conditions for the attainment of these bounds are specified in terms of the input power spectrum. Finally, the behavior of the optimum compaction gain as a function of M (the number of channels in a subband coder) is also addressed.