Efficient signal extension for subband/wavelet decomposition of arbitrary-length signals
Herjan J. Barnard, Jos H. Weber, Jan Biemond · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
Compression of digital signals is often performed with a two-band subband/wavelet decomposition scheme. Conventional tree-structured schemes with depth k that are based on this two-channel scheme require an input signal of which the length is a multiple of 2k. Normally, if the input signal does not meet this condition, samples are added to it until the requirement is met. However, these extra samples lead to an increase in data. In this paper a new method is presented that is based on an efficient way of signal extension. With this method, signals of arbitrary length N can be decomposed into subbands up to arbitrary level without an increase in data. Furthermore, a new alternative boundary extension method for filtering even length signals with symmetric odd length filters is presented. This so-called symmetric-periodic extension is closely related to the new efficient signal extension method and has the advantage of having periodicity 2N. In this paper all signal extensions are explained visually with diagrams to clearly demonstrate perfect reconstruction conditions.