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A new fast algorithm for the unified forward and inverse MDCT/MDST computation. (English) Zbl 1007.94521
Summary: 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. Princen, Bradley and Johnson defined two types of the MDCT, specifically, for an evenly stacked and oddly stacked analysis/synthesis system. 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 for the fast MDCT computation. A 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, and real arithmetic is used only. The corresponding generalized signal flow graph is regular, structurally simple and enables MDCT/MDST and their inverses to be computed in general for any $$N$$ divisible by 4 ($$N$$ being the 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 the MPEG family, and in commercial products (proprietary audio coding algorithms). Besides, the new fast algorithm has some interesting properties, and 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 $$N\neq 2^{n}$$. 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 and generalized discrete Hartley transform of type IV can be used for the fast alternate or simultaneous (on-line) MDCT/MDST computation by simple pre- and post-processing of data sequences.

##### MSC:
 94A12 Signal theory (characterization, reconstruction, filtering, etc.) 65T50 Numerical methods for discrete and fast Fourier transforms
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