Audio Signal Processing and Coding

6.4 QUADRATURE MIRROR AND CONJUGATE QUADRATURE FILTERS

The two-band quadrature mirror and conjugate quadrature filter (QMF and CQF) banks are logical starting points for the discussion on filter banks for audio coding. Two-band QMF banks were used in early subband algorithms for speech coding [Croc76], and later for the first standardized 7-kHz wideband audio algorithm, the ITU G.722 [G722]. Also, the strong connection between two-band perfect reconstruction (PR) CQF filter banks and the discrete wavelet transform [Akan96] has played a significant role in the development of high-performance audio coding filter banks. Ultimately, tree-structured cascades of the CQF filters have been used to construct several “critical-band” filter banks in a number of high quality algorithms. The two-channel bank, which can provide a building block for structured M-channel banks, is developed as follows. If the analysis-synthesis filter bank (Figure 6.1) is constrained to two channels, i.e., if M = 2, then Eq. (6.5) becomes

Esteband and Galand showed [Este77] that aliasing is cancelled between the upper and lower bands if the QMF conditions are satisfied, namely

Thus, the two-band filter-bank design task is reduced to the design of a single, lowpass filter, h₀(n), under the constraint that the overall ...