ABSTRACT
Most of these audio compression schemes adopted the Modified Discrete Cosine Transform (MDCT) and its inverse Transform (IMDCT). The MDCT and IMDCT are employed in the sub-band/transform coding schemes as the analysis/synthesis filter bank based on time domain aliasing cancellation (TDAC).
This dominance of the MDCT can be observed from the audio coding schemes as standardized by the Motion Picture Expert Group (MPEG) of the International Standardization Organization (ISO), such as MPEG-1 layer 3 [1] (MP3) and MPEG-2/4 AAC [2, 3] formats, and from Dolby AC-3 [4] (”Dolby Digital”) as standardized by the Advanced Television Systems Committee (ATSC).
Because the block lengths for MDCT employed filterbank of MPEG-4 AAC required in DRM standard [5] are 1920 and 240, this thesis proposes a fast algorithm for modified discrete cosine transform (MDCT) for transform lengths of the form 1920 and 240 by using mixed-radix algorithm. This mixed-radix algorithm based-on combining radix-2, radix-3, and radix-5 MDCT algorithms.
The algorithm is useful for MDCT computation of length 1920/240, it also uses very efficiently for transform lengths that have a factor of 30 such as 60, 120, 480, and 960 in other modes of the MPEG-4 AAC standard.

REFERENCES
[1] "ISO/IEC 11172-3: 1993. Information technology -- Coding of moving pictures and associated audio for digital storage media at up to about 1,5 Mbit/s -- Part 3: Audio," ed, 1993.
[2] "ISO/IEC 13818-7:2006. Information technology -- Generic coding of moving pictures and associated audio information -- Part 7: Advanced Audio Coding (AAC)," ed, 2006.
[3] "ISO/IEC 14496-3. Information technology — Coding of audio-visual objects — Part 3: Audio, Third edition," ed, 2005.
[4] "ATSC A/52:2012: Digital Audio Compression (AC-3) (E-AC-3) Standard," 17 December 2012 2012.
[5] "Digital Radio Mondiale (DRM); System Specification," in ETSI ES 201 980 V2.2.1 (2005-10), ed. ETSI Standard, 2005.
[6] F. Hofmann, C. Hansen, and W. Schafer, "Digital Radio Mondiale (DRM) digital sound broadcasting in the AM bands," Broadcasting, IEEE Transactions on, vol. 49, pp. 319-328, 2003.
[7] P. Duhamel, Y. Mahieux, and J. P. Petit, "A fast algorithm for the implementation of filter banks based on `time domain aliasing cancellation'," in Acoustics, Speech, and Signal Processing, 1991. ICASSP-91., 1991 International Conference on, 1991, pp. 2209-2212 vol.3.
[8] C. Mu-Huo and H. Yu-Hsin, "Fast IMDCT and MDCT algorithms - a matrix approach," Signal Processing, IEEE Transactions on, vol. 51, pp. 221-229, 2003.
[9] L. Szu-Wei, "Improved algorithm for efficient computation of the forward and backward MDCT in MPEG audio coder," Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on, vol. 48, pp. 990-994, 2001.
[10] V. Britanak and K. R. Rao, "An efficient implementation of the forward and inverse MDCT in MPEG audio coding," Signal Processing Letters, IEEE, vol. 8, pp. 48-51, 2001.
[11] H. Shu, X. Bao, C. Toumoulin, and L. Luo, "Radix-3 Algorithm for the Fast Computation of Forward and Inverse MDCT," Signal Processing Letters, IEEE, vol. 14, pp. 93-96, 2007.
[12] G. Bi and L. W. Yu, "DCT algorithms for composite sequence lengths," Signal Processing, IEEE Transactions on, vol. 46, pp. 554-562, 1998.
[13] G. Bi and Y. Zeng, "Fast Algorithms for 1D Discrete Cosine Transform," in Transforms and Fast Algorithms for Signal Analysis and Representations, ed: Birkhäuser Boston, 2004, pp. 207-245.
[14] H. Haibin, S. Rahardja, Y. Rongshan, and L. Xiao, "Integer MDCT with enhanced approximation of the DCT-IV," Signal Processing, IEEE Transactions on, vol. 54, pp. 1156-1159, 2006.
[15] H.-W. Hsu and C.-M. Liu, "Fast Radix- <formula> <tex>$q$</tex> </formula> and Mixed-Radix Algorithms for Type-IV DCT," IEEE Signal Processing Letters, vol. 15, pp. 910-913, 2008.
[16] W. Jiasong, S. Huazhong, L. Senhadji, and L. Limin, "Mixed-Radix Algorithm for the Computation of Forward and Inverse MDCTs," Circuits and Systems I: Regular Papers, IEEE Transactions on, vol. 56, pp. 784-794, 2009.
[17] Z. G. Gui, Y. Ge, D. Y. Zhang, and J. S. Wu, "Generalized fast mixed-radix algorithm for the computation of forward and inverse MDCTs," Signal Processing, vol. 92, pp. 363-373, 2// 2012.
[18] J. Princen, A. Johnson, and A. Bradley, "Subband/Transform coding using filter bank designs based on time domain aliasing cancellation," in Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP '87., 1987, pp. 2161-2164.
[19] V. Britanak, "Improved and Extended Mixed-Radix Decimation in Frequency Fast MDCT Algorithm," presented at the Computing and Informatics, 2010.
[20] W. Jiasong, W. Lu, L. Senhadji, and S. Huazhong, "Improved radix-3 decimation-in-frequency algorithm for the fast computation of forward and inverse MDCT," in Audio Language and Image Processing (ICALIP), 2010 International Conference on, 2010, pp. 694-699.
[21] V. Britanak, "A survey of efficient MDCT implementations in MP3 audio coding standard: Retrospective and state-of-the-art," Signal Processing, vol. 91, pp. 624-672, 4// 2011.
[22] D.-S. Ku, J.-H. Yun, and J.-B. Kim, "A Design on the Vector Processor of 2048point MDCT/IMDCT for MPEG-2 AAC," in Advances in Natural Computation. vol. 3612, L. Wang, K. Chen, and Y. Ong, Eds., ed: Springer Berlin Heidelberg, 2005, pp. 1032-1043.