Handling finite length signals borders in two-channel multirate filter banks for perfect reconstruction

Perfect reconstruction multirate filter banks theory was built on the assumption of infinite length signals. For processing limited support signals, e.g. an image, discontinuities exist at the signal border. The problem of which values to use at these boundaries cannot be ignored if perfect reconstruction is required. This paper presents our own investigation into the different techniques adopted to deal with this problem. It shows precisely what type of borders management should be applied and especially how, according to the underlying constraints to ensure perfect reconstruction two-channel multirate filter banks implementation on finite length signals with a zero-delay transfer function. This gives numerically the minimum number of extra samples to be added at the signal's and subband's edges; a vital issue for many filter-banks-based architectures like with the discrete wavelet transform (DWT).