Fast Algorithms for Low-Delay TDAC Filterbanks in MPEG-4 AAC-ELD

Abstract—The MPEG committee has completed development of a new audio coding standard called “MPEG-4 advanced audio coding–enhanced low delay ” (AAC-ELD). AAC-ELD uses low delay spectral band replication (LD-SBR) technology together with a low delay time domain alias cancellation (LD TDAC) fil-terbank in the encoder to achieve both high coding efficiency and low algorithmic delay. In this paper, we present fast algorithms for implementing LD-TDAC filterbanks in AAC-ELD. Two types of fast algorithms are presented. In the first, we map LD-TDAC analysis and synthesis filterbanks to modified discrete cosine transform (MDCT) and inverse modified discrete cosine trans-form (IMDCT), respectively. Since MDCT/IMDCT are already extensively used in AAC and they have many fast algorithms, this mapping not only provides a fast implementation but also allows a common implementation of the filterbanks in AAC Low Com-plexity (AAC-LC), AAC Low Delay (AAC-LD) and AAC-ELD codecs. In the second algorithm, we provide a mapping to discrete Cosine transform of type II. The mapping to DCT-II allows the merger of the matrix operations with the windowing stage that precedes or follows them. This further reduces the number of multiplications and leads to an algorithm with the lowest known arithmetic complexity. For filterbanks of lengths 1024 and 960, we also present a new fast factorization of 15-point DCT-II that requires only 14 irrational multiplications, 3 dyadic rational multiplications and 67 additions. Index Terms—AAC, audio coding, DCT, factorization, fast algo