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Fast computational structures for an efficient implementation of the complete TDAC analysis/synthesis MDCT/MDST filter banks

Fast computational structures for an efficient implementation of the complete TDAC analysis/synthesis MDCT/MDST filter banks,10.1016/j.sigpro.2009.01.

Fast computational structures for an efficient implementation of the complete TDAC analysis/synthesis MDCT/MDST filter banks   (Citations: 5)
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A new fast computational structure identical both for the forward and backward modified discrete cosine/sine transform (MDCT/MDST) computation is described. It is the result of a systematic construction of a fast algorithm for an efficient implementation of the complete time domain aliasing cancellation (TDAC) analysis/synthesis MDCT/MDST filter banks. It is shown that the same computational structure can be used both for the encoder and the decoder, thus significantly reducing design time and resources. The corresponding generalized signal flow graph is regular and defines new sparse matrix factorizations of the discrete cosine transform of type IV (DCT-IV) and MDCT/MDST matrices. The identical fast MDCT computational structure provides an efficient implementation of the MDCT in MPEG layer III (MP3) audio coding and the Dolby Labs AC-3 codec. All steps to derive the computational structure are described in detail, and to put them into perspective a comprehensive list of references classified into categories is provided covering new research results achieved in the time period 1999–2008 in theoretical and practical developments of TDAC analysis/synthesis MDCT/MDST filter banks (general mathematical, symmetry and special properties, fast MDCT/MDST algorithms and efficient software/hardware implementations of the MDCT in MP3).
Journal: Signal Processing , vol. 89, no. 7, pp. 1379-1394, 2009
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    • ...Motivated by a specific definition of AC-3 filter banks, some existing fast algorithms and fast computational structures for the discrete sinusoidal unitary transforms computation of real data sequences as well as new proposed fast MDCT algorithms have been investigated for the alternate and simultaneous (online) efficient implementation of AC-3 transforms [9]‐[12]...
    • ...The symmetry properties of data sequences and as well as the general mathematical and special properties of the MDCT block transform are presented in [12]...
    • ...Essentially, the forward and backward MDCT blocktransformwiththewindowingoperationcanbeefficiently realized by the fast analysis and synthesis MDCT filter banks based on an -point DCT-IV [12]...
    • ...For its arithmetic complexity is real multiplications and realadditions[12].ThebackwardMDCT computation requires exactly less real additions...
    • ...There exists a simple relation between the MDCT and the MDST [11], [12],andtherefore,theforwardMDSTcomputationintheAC-3 (E-AC-3) encoder can be realized by the same -point forwardcomplexFFTmoduleonlybysimplepre-processingofthe original input data sequence ...
    • ...The matrix formulation is a very elegant and rigorous tool to represent and investigate mathematical properties of any perfect reconstruction cosine-/sine-modulated filter bank [12], [15]...
    • ...In order to ensure TDAC, the windowing functions of two succeeding data blocks have to satisfy the so-called perfect reconstruction conditions. They are given by [12]...
    • ...Then, the forward and backward MDCT block transforms given by (5) and (6), respectively, including the windowing operation and the normalization factor can be written in the equivalent matrix-vector form as [12]...
    • ...For products of the matrix and its pseudoinverse, , the following relations hold [12], [15]:...
    • ...We recall that the th row basis vector of in the first half possesses the even anti-symmetry and in the second half possesses the even symmetry property, respectively, given by [12]...

    Vladimir Britanak. On Properties, Relations, and Simplified Implementation of Filter Bank...

    • ...In the past decade, many fast algorithms have been reported in the literature (see, e.g., [5], [6] for a survey)...
    • ...The comparison of the advantages and disadvantages of these MDCT-based algorithms with the DCT-based algorithms [5-14], we refer the readers to [15] and [16]...

    Jiasong Wuet al. Improved radix-3 decimation-in-frequency algorithm for the fast comput...

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