Open Access
Improved integer transforms using multi-dimensional lifting
Ralf Geiger,Yoshikazu Yokotani,Gerald Schuller,Jürgen Herre +3 more
- 01 Jan 2004
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TL;DR: This paper presents a multidimensional lifting approach for reducing approximation error in the frequency domain of lifting-based integer transforms, where large parts of the transform are calculated without rounding operations, only the output is rounded and added.
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Abstract: Recently lifting-based integer transforms have received much attention, especially in the area of lossless audio and image coding. The usual approach is to apply the lifting scheme to each Givens rotation. Especially in the case of long transform sizes in audio coding applications, this leads to a considerable approximation error in the frequency domain. This paper presents a multidimensional lifting approach for reducing this approximation error. In this approach, large parts of the transform are calculated without rounding operations, only the output is rounded and added. The new approach is applied and evaluated for both the Integer Modified Discrete Cosine Transform (IntMDCT) and the Integer Fast Fourier Transform (IntFFT).
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Citations
CHAPTER 5 – Integer Discrete Cosine/Sine Transforms
Vladimir Britanak,Patrick C. Yip,K. R. Rao +2 more
- 01 Jan 2006
TL;DR: The discrete cosine transforms (DCTs) and discrete sine transform (DSTs) are real-valued transforms that map integer-valued signals to floating-point coefficients as discussed by the authors.
43
•Journal Article
ISO/IEC MPEG-4 High-Definition Scalable Advanced Audio Coding
TL;DR: The underlying innovative technology is described in detail and its performance is characterized for lossless and near lossless representation, both in conjunction with an AAC coder and as a stand-alone compression engine.
38
•Proceedings Article
Integer sub-optimal Karhunen-Loeve transform for multi-channel lossless EEG compression
Yodchanan Wongsawat,Soontorn Oraintara,K.R. Rao +2 more
- 01 Sep 2006
TL;DR: A method for approximating the Karhunen-Loeve Transform (KLT) for the purpose of multi-channel lossless electroencephalogram (EEG) compression yields a near optimal transform for the case of Markov process, but significantly reduces the computational complexity.
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Lossless Audio Coding Using the IntMDCT and Rounding Error Shaping
TL;DR: In this paper, lossless audio coding using the integer modified discrete cosine transform (IntMDCT) is discussed and a method for shaping the rounding error in the transform domain is presented.
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New universal rotation-based fast computational structures for an efficient implementation of the DCT-IV/DST-IV and analysis/synthesis MDCT/MDST filter banks
TL;DR: Since Givens-Jacobi rotation can be factored into a product of Gauss elementary matrices being unit lower and unit upper triangular matrices, the new fast rotation-based computational structures are suitable for an integer approximation of the DCT-IV/DST-IV and MDCT/MDST which are currently modern transform technologies for lossless audio coding.
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References
On computing the inverse DFT
TL;DR: The authors indicate an apparently novel method for computing an inverse discrete Fourier transform (IDFT) through the use of a forward DFT program, and point out that, in many cases, this is obtained without any additional cost, either in terms of program length or in Terms of computational time.
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Improved integer transforms for lossless audio coding
Ralf Geiger,Yoshikazu Yokotani,Gerald Schuller +2 more
- 09 Nov 2003
TL;DR: This paper will propose structures for improved integer transforms in terms of improved approximation accuracy and computational efficiency, and Experimental results will show that clear improvements in these two points are achieved in lossless audio coding.
1-D and 2-D transforms from integers to integers
TL;DR: A new kind of matrix decomposition method called lifting-like factorization is introduced, which leads to a theorem: every 2/sup n/-order real matrix with determinant norm 1 can be expressed as the product of one permutation matrix and at most three unit triangular matrices.
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Integer low delay and MDCT filter banks
Ralf Geiger,Gerald Schuller +1 more
- 03 Nov 2002
TL;DR: Application of the techniques to cosine modulated filter banks for audio coding, including not only the modified discrete Fourier transform (MDCT) but also low delay filter banks are focused on.
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Lossless audio compression using integer modified discrete cosine transform
Yoshikazu Yokotani,Soontorn Oraintara,Awaji Island +2 more
- 01 Jan 2003
TL;DR: There exists a trade-off between computational complexity and coding efficiency when it is applied in the MPEG2 AAC based lossless audio coding scheme and one can reduce the computational complexity of the IntMDCT while a certain level of coding efficiency is maintained in the scheme.
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