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General sub-band DCT: fast approximate adaptive algorithm. (English) Zbl 1055.65151

Procházka, A. (ed.) et al., Signal analysis and prediction. Based upon selected contributions presented at the 1st European conference on signal analysis and prediction, ECSAP-97, Prague, Czech Republic. Boston, MA: Birkhäuser (ISBN 0-8176-4042-8/hbk). Applied and Numerical Harmonic Analysis, 47-56 (1998).
Summary: The discrete cosine transform (DCT) has a variety of applications in image and speech coding. The idea of the approximate subband discrete Fourier transform [cf. S. K. Mitra, O. V. Shentov and M. R. Petraglia, A method for fast approximate computation of discrete time transforms, in Proc. of ICASSP ’90, Albuquerque, NM, 2025–2028 (1990); A. N. Hossen, U. Heute, O. Shentov and S. Mitra, Signal Process. 41, No. 3, 279–294 (1995; Zbl 0872.94003)] is applied by S. Jung, S. Mitra and D. Mukherjee [Subband DCT: Definition, analysis, and applications, IEEE Trans. on Circuits and Systems for Video Technology, 6, No. 3 (1996); A. N. Hossen and U. Heute, Fast approximate DCT: Basic-idea, error analysis, applications, in Proc. of ICASSP ’97, Munich, Germany (1997)] to the DCT.
In this paper the basic idea of the subband DCT (SB-DCT) is reviewed. The calculation of the approximate SB-DCT is done with the aid of a fast cosine-transform method. The subband DCT is generalized such that any band out of \(M\) subbands can be calculated. For this purpose the fast DCT method is modified to calculate the fast discrete subband transform. A general analysis of the errors due to the approximation is presented. The adaptive capability of the SB-DFT given by A. N. Hossen and U. Heute [Fully adaptive evaluation of the subband DFT, in Proc. of ISCAS ’93, Chicago, 655–658 (1993)] is added to the SB-DCT to calculate adaptively the band of the dominant energy. The two-dimensional SB-DCT is also investigated in this work. Applications of the general adaptive SB-DCT in speech cepstrum analysis and in echo detection are included.
For the entire collection see [Zbl 0904.00062].

MSC:

65T50 Numerical methods for discrete and fast Fourier transforms
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)

Citations:

Zbl 0872.94003
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