J. P. Princen and A. B. Bradley, Analysis/Synthesis filter bank design based on time domain aliasing cancellation, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.34, issue.5, pp.1153-1161, 1986.
DOI : 10.1109/TASSP.1986.1164954

J. P. Princen, A. W. Johnson, and A. B. Bradley, Subband/Transform coding using filter bank designs based on time domain aliasing cancellation, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.2161-2164, 1987.
DOI : 10.1109/ICASSP.1987.1169405

H. S. Malvar, Signal Processing with lapped transforms, Artech House, 1992.
DOI : 10.1109/icassp.1990.115698

Y. T. Hwang and S. C. Lai, A novel MDCT/IMDCT computing kernel design, IEEE SIPS, pp.526-531, 2005.

M. Iwadare, A. Sugiyama, F. Hazu, A. Hirano, and T. Nishitani, A 128 Kb/s Hi-Fi audio codec based on adaptive transform coding with adaptive block size MDCT, IEEE Journal on Selected Areas in Communications, vol.10, issue.1, pp.138-144, 1992.
DOI : 10.1109/49.124473

Y. H. Fan, V. K. Madisetti, and R. M. Mersereau, On fast algorithms for computing the inverse modified discrete cosine transform, IEEE Signal Process. Lett, vol.6, issue.3, pp.61-64, 1999.

V. Britanak and K. R. Rao, An efficient implementation of the forward and inverse MDCT in MPEG audio coding, IEEE Signal Processing Letters, vol.8, issue.2, pp.48-51, 2001.
DOI : 10.1109/97.895372

V. Britanak and K. R. Rao, A new fast algorithm for the unified forward and inverse MDCT/MDST computation, Signal Processing, vol.82, issue.3, pp.433-459, 2002.
DOI : 10.1016/S0165-1684(01)00195-5

S. W. Lee, Improved algorithm for efficient computation of the forward and backward MDCT in MPEG audio coder, IEEE Trans. Circuits Syst.-II: Analog Digital Signal Processing, vol.48, issue.10, pp.990-994, 2001.

C. Y. Jing and H. M. Tai, Fast algorithm for computing modulated lapped transform, Electronics Letters, vol.37, issue.12, pp.796-797, 2001.
DOI : 10.1049/el:20010539

M. H. Cheng and Y. H. Hsu, Fast IMDCT and MDCT algorithms - a matrix approach, IEEE Transactions on Signal Processing, vol.51, issue.1, pp.221-229, 2003.
DOI : 10.1109/TSP.2002.806566

T. K. Truong, P. D. Chen, and T. C. Cheng, Fast algorithm for computing the forward and inverse MDCT in MPEG audio coding, Signal Processing, vol.86, issue.5, pp.1055-1060, 2006.
DOI : 10.1016/j.sigpro.2005.07.027

X. Shao and S. G. Johnson, Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations, Signal Processing, vol.88, issue.6, pp.1313-1326, 2008.
DOI : 10.1016/j.sigpro.2007.11.024

S. G. Johnson and M. Frigo, A Modified Split-Radix FFT With Fewer Arithmetic Operations, IEEE Transactions on Signal Processing, vol.55, issue.1, pp.111-119, 2007.
DOI : 10.1109/TSP.2006.882087

V. Britanak, An efficient computing of oddly stacked MDCT/MDST via evenly stacked MDCT/MDST and vice versa, Signal Processing, vol.85, issue.7, pp.1353-1374, 2005.
DOI : 10.1016/j.sigpro.2005.02.001

S. Bouguezel, M. O. Ahmad, and M. N. Swamy, A New Radix-<tex>$2/8$</tex>FFT Algorithm for Length-<tex>$qtimes 2^m$</tex>DFTs, IEEE Transactions on Circuits and Systems I: Regular Papers, vol.51, issue.9, pp.1723-1732, 2004.
DOI : 10.1109/TCSI.2004.834508

P. Duhamel and M. Vetterli, Fast Fourier Transforms, Signal Process, vol.19, issue.4, pp.259-299, 1990.
DOI : 10.1201/9781420046076-c7

P. K. Meher, Efficient Systolic Implementation of DFT Using a Low-Complexity Convolution-Like Formulation, IEEE Transactions on Circuits and Systems II: Express Briefs, vol.53, issue.8, pp.702-706, 2006.
DOI : 10.1109/TCSII.2006.875379

C. Cheng and K. K. Parhi, Low-Cost Fast VLSI Algorithm for Discrete Fourier Transform, IEEE Transactions on Circuits and Systems I: Regular Papers, vol.54, issue.4, pp.791-806, 2007.
DOI : 10.1109/TCSI.2006.888772

C. W. Kok, Fast algorithm for computing discrete cosine transform, IEEE Transactions on Signal Processing, vol.45, issue.3, pp.757-760, 1997.
DOI : 10.1109/78.558495

Y. H. Chan and W. C. Siu, Mixed-radix discrete cosine transform, IEEE Transactions on Signal Processing, vol.41, issue.11, pp.3157-3161, 1993.
DOI : 10.1109/78.257281

G. Bi and L. W. Yu, DCT algorithms for composite sequence lengths, IEEE Transactions on Signal Processing, vol.46, issue.3, pp.554-562, 1998.
DOI : 10.1109/78.661324

V. Britanak, P. Yip, and K. R. Rao, Discrete cosine and sine transforms: general properties, fast algorithms and integer approximations, 2007.

P. K. Meher, Unified Systolic-Like Architecture for DCT and DST Using Distributed Arithmetic, IEEE Transactions on Circuits and Systems I: Regular Papers, vol.53, issue.12, pp.2656-2663, 2006.
DOI : 10.1109/TCSI.2006.885978

K. A. Wahid, V. S. Dimitrov, and G. A. Jullien, On the Error-Free Realization of a Scaled DCT Algorithm and Its VLSI Implementation, IEEE Transactions on Circuits and Systems II: Express Briefs, vol.54, issue.8
DOI : 10.1109/TCSII.2007.898891

T. C. Tan, G. Bi, Y. Zeng, and H. N. Tan, DCT hardware structure for sequentially presented data, Signal Processing, vol.81, issue.11, pp.2333-2342, 2001.
DOI : 10.1016/S0165-1684(01)00113-X

H. C. Chiang and J. C. Liu, Regressive implementations for the forward and inverse MDCT in MPEG audio coding, IEEE Signal Processing Letters, vol.3, issue.4, pp.116-118, 1996.
DOI : 10.1109/97.489065

C. H. Chen, B. D. Liu, and J. F. Yang, Recursive architectures for realizing modified discrete cosine transform and its inverse, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol.50, issue.1, pp.38-44, 2003.
DOI : 10.1109/TCSII.2003.808895

V. Nikolajevic and G. Fettweis, Computation of forward and inverse MDCT using clenshaw's recurrence formula, IEEE Transactions on Signal Processing, vol.51, issue.5, pp.1439-1444, 2003.
DOI : 10.1109/TSP.2002.808123

H. Shu, X. Bao, C. Toumoulin, and L. Luo, Radix-3 Algorithm for the Fast Computation of Forward and Inverse MDCT, IEEE Signal Processing Letters, vol.14, issue.2, pp.93-96, 2007.
DOI : 10.1109/LSP.2006.882108

URL : https://hal.archives-ouvertes.fr/hal-00141445

T. Krishnan and S. Oraintara, Fast and lossless implementation of the forward and inverse MDCT computation in MPEG audio coding, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353), pp.181-184, 2002.
DOI : 10.1109/ISCAS.2002.1010954

H. D. Yun and S. U. Lee, On the fixed-point-error analysis of several fast DCT algorithms, IEEE Trans. Circuits Syst. Video Technol, vol.3, pp.27-41, 1993.

J. S. Wu, H. Z. Shu, L. Senhadji, and L. M. Luo, A fast algorithm for the computation of 2-D forward and inverse MDCT, Signal Processing, vol.88, issue.6, pp.1436-1446, 2008.
DOI : 10.1016/j.sigpro.2007.12.003

URL : https://hal.archives-ouvertes.fr/hal-00271377

O. Lashko, Modulated lapped transform: application in image coding and effective algorithm of its realization, Modern Problems of Radio Engineering, Telecommunications and Computer Science (IEEE Cat. No.02EX542), pp.243-244, 2002.
DOI : 10.1109/TCSET.2002.1015946

N. C. Tungala and A. Noore, Elimination of visual artifacts in digital image watermarking, Proceedings of the 35th Southeastern Symposium on System Theory, 2003., pp.64-68, 2003.
DOI : 10.1109/SSST.2003.1194531

D. Pan, A tutorial on MPEG/audio compression, IEEE Multimedia, vol.2, issue.2, pp.60-74, 1995.
DOI : 10.1109/93.388209

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.126.1881

. Fig, 1. Flowgraph of a length-8 MDCT (radix-2 DIF)

. Fig, Flowgraph of a length-6 MDCT (a) and a length-6 IMDCT (b). " ° " signifies that input is set to zero or output equals to zero