February 2007
Intermediate to advanced
464 pages
14h 40m
English
Content preview from Audio Signal Processing and CodingBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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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 ...
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