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Keywords
(13)
Audio Coding
Discrete Cosine Transform
Efficient Implementation
Fast Algorithm
Hardware Implementation
Sparse Matrix
Discrete Sine Transform
Filter Bank
Modulated Complex Lapped Transform
Modified Discrete Cosine Transform
Modulated Lapped Transform
Signal Flow Graph
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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.
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Fast computational structures for an efficient implementation of the complete TDAC analysis/synthesis MDCT/MDST filter banks
(
Citations: 5
)
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Vladimir Britanak
,
Huibert J. Lincklaen Arriëns
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 (DCTIV) 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 AC3 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. 13791394, 2009
DOI:
10.1016/j.sigpro.2009.01.014
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Citation Context
(2)
...Motivated by a specific definition of AC3 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 AC3 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 DCTIV [
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,theforwardMDSTcomputationintheAC3 (EAC3) encoder can be realized by the same point forwardcomplexFFTmoduleonlybysimplepreprocessingofthe 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/sinemodulated filter bank [
12
], [15]...
...In order to ensure TDAC, the windowing functions of two succeeding data blocks have to satisfy the socalled 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 matrixvector 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 antisymmetry 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 MDCTbased algorithms with the DCTbased algorithms [
514
], we refer the readers to [15] and [16]...
Jiasong Wu
,
et al.
Improved radix3 decimationinfrequency algorithm for the fast comput...
References
(32)
Perceptual coding of digital audio
(
Citations: 304
)
Ted Painter
,
Andreas Spanias
Journal:
Proceedings of The IEEE  PIEEE
, vol. 88, no. 4, pp. 451515, 2000
Introduction to Digital Audio Coding and Standards
(
Citations: 82
)
Marina Bosi
,
Richard E. Goldberg
,
Joan L. Mitchell
Journal:
Journal of Electronic Imaging  JEI
, vol. 13, no. 2, pp. 399400, 2004
Audio Signal Processing and Coding
(
Citations: 21
)
Andreas Spanias
,
Ted Painter
,
Venkatraman Atti
,
James V. Candy
Journal:
Journal of The Acoustical Society of America  J ACOUST SOC AMER
, vol. 122, no. 1, 2007
THE MODIFIED DISCRETE COSINE TRANSFORM: ITS IMPLICATIONS FOR AUDIO CODING AND ERROR CONCEALMENT
(
Citations: 23
)
Ye Wang
,
Miikka Vilermo
Journal:
Advances in Engineering Software  AES
A Note on the MDCT/MDST and Pseudoinverse Matrix
(
Citations: 2
)
Vladimir Britanak
Journal:
Computing and Informatics / Computers and Artificial Intelligence  CAI
, vol. 23, no. 3, 2004
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Citations
(5)
A survey of efficient MDCT implementations in MP3 audio coding standard: Retrospective and stateoftheart
Vladimir Britanak
Journal:
Signal Processing
, vol. 91, no. 4, pp. 624672, 2011
On Properties, Relations, and Simplified Implementation of Filter Banks in the Dolby Digital (Plus) AC3 Audio Coding Standards
Vladimir Britanak
Journal:
IEEE Transactions on Audio, Speech & Language Processing  TASLP
, vol. 19, no. 5, pp. 12311241, 2011
New fast computational structures for an efficient implementation of the forward/backward MDCT in MP3 audio coding standard
(
Citations: 1
)
Vladimir Britanak
Journal:
Signal Processing
, vol. 90, no. 2, pp. 536547, 2010
Improved radix3 decimationinfrequency algorithm for the fast computation of forward and inverse MDCT
Jiasong Wu
,
Lu Wang
,
Lotfi Senhadji
,
Huazhong Shu
Conference:
International Conference on Audio, Language and Image Processing  ICALIP
, 2010
New universal rotationbased fast computational structures for an efficient implementation of the DCTIV/DSTIV and analysis/synthesis MDCT/MDST filter banks
(
Citations: 4
)
Vladimir Britanak
Journal:
Signal Processing
, vol. 89, no. 11, pp. 22132232, 2009