Performance evaluation of subband coding and optimization of its filter coefficients

In this paper, two analytical methods for evaluating the coding efficiency of subband coding are proposed, and optimization of filter coefficients of the perfect reconstruction FIR filter banks is considered, based on a new performance measure called unified coding gain. First, matrix representation of the subband coding in the time domain is considered, and conventional subband filter banks are classified into orthogonal ones such as the QMF and nonorthogonal ones such as the SSKF. For the orthogonal filter banks, the coding gain shown by Jayant and Noll is introduced, and their theoretical performance evaluation is carried out. However, this first method cannot be applied to nonorthogonal filter banks any longer because the coding gain is defined on the assumption of filter orthogonality. Therefore, an optimum bit allocation problem for subband coding is considered, and the unified coding gain, which can be applied to arbitrary subband filter banks, is derived as a new performance measure to take the place of the coding gain. This second method enables us to estimate the coding efficiency of arbitrary transform techniques as well as the subband approaches, and its result suggests that the SSKF(5 × 3) outperforms the QMF as long as the number of subbands is not too large, even though its filter length is much shorter. This result encourages us to find filter coefficients that maximize the unified coding gain according to filter length. In addition, new perfect reconstruction FIR filter banks which have not only low computational complexity but also good energy compaction properties are presented.