Cosine-Sine-Modulated Filter Banks by Vladimir Britanak & K. R. Rao

Author:Vladimir Britanak & K. R. Rao
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(5.198)

Again, (5.198) represents the 2-point Hankel matrix-vector product. The corresponding compact computational structure of the fast TDAC synthesis MDCT filter bank with incorporated windowing&overlap&add procedure for arbitrary symmetric windowing function {w n } can be obtained from Fig. 5.26b by setting constants m 1,  m 2 and m 3 to the following values

(5.199)

5.6 Summary

Various efficient implementations of the forward and backward MDCT (MLT) block transforms in the MP3 audio coding standard developed in the time period 1990–2012 have been described and compared, including the efficient implementation of (pseudo-) QMF filter banks for completeness. The efficient MDCT (MLT) implementations have been discussed in the context of complete (fast) TDAC analysis/synthesis MDCT filter banks associated with the sine windowing function or equivalently, of the fast analysis/synthesis MLT filter banks in the MP3 encoder and decoder. For each efficient implementation of the forward/backward MDCT (MLT), block transforms have been presented: complete formulae or sparse matrix factorizations, the corresponding signal flow graph for short audio block, and the total arithmetic complexity as well as useful comments related to improving the arithmetic complexity and a possible structural simplification of the algorithm. Finally, the fast TDAC analysis/synthesis MDCT filter banks or equivalently, the fast analysis/synthesis MLT filter banks for MP3 encoder/decoder have been discussed in detail. Appendices provide all the necessary supporting efficient optimized short-length computational modules and tools for completing efficient forward/backward MDCT (MLT) implementations. Essentially, the chapter provides: Efficient implementations of the hybrid analysis/synthesis filter banks in MP3 audio coding standard.

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