Efficient Implementations of Perfect Reconstruction Low Delay Cosine-Modulated Filter Banks in the MPEG-4 AAC-ELD

Abstract

The MPEG committee has recently completed development of a new audio coding standard, the MPEG-4 Advanced Audio Coding-Enhanced Low Delay (AAC-ELD). State-of-the-art MPEG audio coding standards, such as MPEG-4 AAC Low Complexity (AAC-LC), High Efficiency AAC (HE-AAC), and AAC Low Delay (AAC-LD), utilize the time-to-frequency transformation of an audio block and vice versa, the well-known time domain aliasing cancellation modified discrete cosine transform (TDAC-MDCT). In order to achieve low algorithmic delay, the AAC-ELD has adopted a perfect reconstruction low delay cosine-modulated filter bank, called the low delay MDCT (LD-MDCT). Although the use of LD-MDCT substantially reduces the algorithmic delays, the transform operations in the AAC-ELD codec are still computationally intensive and the LD-MDCT filter banks need to have fast algorithms. Therefore, this chapter is concentrated on the analysis/synthesis LD-MDCT filter banks used the AAC-ELD codec and mainly on their efficient implementations. This chapter presents: Definitions of the analysis/synthesis LD-MDCT (and TDAC-MDCT) filter banks, general symmetry properties of LD-MDCT transforms both in the time and frequency domains, relations between the LD-MDCT and TDAC-MDCT transforms in the analytical forms as well as in the equivalent matrix representations, and efficient implementations of the even-length analysis/synthesis LD-MDCT filter banks. For each fast LD-MDCT algorithm the complete formulae are derived. All the fast even-length LD-MDCT algorithms are investigated and compared in terms of arithmetic complexity and structural simplicity.