Optimal construction of filter banks for subband coding of quantised signals

Abstract

A new general method is presented for the analysis of the effects of quantisation and transmission noise in subband filter bank coders. Using general statistical noise characterisation, the filter banks are obtained, which are optimal in the sense of minimising the variance of the difference of the reconstructed signal from the original. It is shown that these are not identical to those achieving perfect reconstruction in lossless coding. A general method is described for the optimal selection of the synthesis filters if the analysis filters and quantisers are given. Assumming the use of these optimal synthesis filters, a method is developed for the determination of the optimal analysis filters and the optimal bit allocation to the subbands. The effects of quantisation on perfect reconstruction filter banks are analysed next, and an explicit expression is determined for the quantiser noise-to-signal ratio for such banks. Given arbitrary quantisers, the analysis filters which are optimal in the sense of minimising the output noise power are obtained. Finally, the jointly optimal selection is determined for the analysis filters and the bit allocations of the subbands. It is seen that this selection is identical to that determined for the theoretically optimal filter banks.