Boundary filters for size-limited paraunitary filter banks with maximum coding gain and ideal DC behavior

This paper presents boundary optimization techniques for the processing of arbitrary-length signals with paraunitary multirate filter banks. The boundary filters are designed to maximize the coding gain while providing an ideal DC behavior where all filters except the low-pass filters have zero mean. Moreover, solutions are presented that have similar frequency responses as the original subband filters. The proposed methods give direct solutions to the problem of finding the optimal boundary filters with maximum coding gain and do not require numerical optimization. Thus, they are even applicable to systems with a large number of subbands and/or very long filter impulse responses.