A new fast algorithm for the unified forward and inverse MDCT/MDST computation

The modified discrete cosine transform (MDCT) and modified discrete sine transform (MDST) are employed in subband/transform coding schemes as the analysis/synthesis filter banks based on the concept of time domain aliasing cancellation (TDAC). Princen, Bradley and Johnson defined two types of the MDCT, specifically, for an evenly stacked and oddly stacked analysis/synthesis systems. The MDCT is the basic processing component in the international audio coding standards and commercial products for high-quality audio compression. Almost all existing audio coding systems have used the complex-valued or real-valued FFT algorithms, and the DCT/DST of type IV (DCT-IV/DST-IV) for the fast MDCT computation. New fast and efficient algorithm for a unified forward and inverse MDCT/MDST computation in the oddly stacked system is proposed. It is based on the DCT/DST of types II and III (DCT-II/DST-II, DCT-III/DST-III), and the real arithmetic is used only. Corresponding generalized signal flow graph is regular, structurally simple and enables to compute MDCT/MDST and their inverses in general for any N divisible by 4 (N being length of a data sequence). Consequently, the new fast algorithm can be adopted for the MDCT computation in the current audio coding standards such as MPEG family (MPEG-1, MPEG-2, MPEG-2 Advanced Audio Coding and MPEG-4 audio), and in commercial products (proprietary audio coding algorithms) such as Sony MiniDisc/ATRAC/ATRAC2/SDDS digital audio coding systems, the AT & T Perceptual Audio Coder (PAC) or Lucent Technologies PAC/Enhanced PAC/Multichannel PAC, and Dolby Labs AC-3 digital audio compression algorithm. Besides the new fast algorithm has some interesting properties, it provides an efficient implementation of the forward and inverse MDCT computation for layer III in MPEG audio coding, where the length of data blocks N ≠ 2n, Especially, for the AC-3 algorithm, it is shown how both the proposed new MDCT/MDST algorithm and existing fast algorithms/computational architectures for the discrete sinusoidal transforms computation of real data sequences such as the DCT-IV/DST-IV, generalized discrete Fourier transform of type IV (DFT-IV) and generalized discrete Hartley transform of type IV (DHT-IV) can be used for the fast alternate or simultaneous (on-line) MDCT/MDST computation by simple pre-and post-processing of data sequences.

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