A generalized fast algorithm for n-D discrete cosine transform and its application to motion picture coding

• Published in: IEEE transactions on circuits and systems. 2, Analog and digital signal processing Vol. 46; no. 5; pp. 617 - 627
• Main Authors: Zhishun Wang, Zhenya He, Cairong Zou, Chen, J.D.Z.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.1999; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Data compression; Discrete cosine transforms; Discrete transforms; Exact sciences and technology; Feature extraction; Image coding; Image processing; Information, signal and communications theory; Motion pictures; Signal processing; Signal processing algorithms; Telecommunications and information theory; Transform coding; Motion picture studio; Computer program; Image processing; Coding circuit; Theoretical study; Signal processing; Performance analysis; Fast algorithm; Multidimensional system; Implementation; Cosine transform
• ISSN: 1057-7130
• DOI: 10.1109/82.769810

In this paper, a generalized fast computational algorithm for the n-dimensional discrete cosine transform (DCT) of length N=2/sup m/ (m/spl ges/2) is presented. The developed algorithm is proved and its efficiency is evaluated theoretically. The theoretical results show that compared with the conventional method of computing the one-dimensional along n directions, the number of multiplications needed by our algorithm is only 1/n of that required by the conventional method; for the total number of additions, the latter is a bit more when N/spl les/8 and much fewer when N/spl ges/16 than the former. To validate the proposed algorithm, we take the case when n=3 as an example and apply it to motion-picture coding. The results show that our method is superior to MPEG-2 in speed and coding performance. The algorithm is clearly described and it is easy to make a computer program for implementation.