CHAPTER 6 CONCLUSION
C.2. Proof of Zeros
To find the MMSE solution of (80), from the geometric symmetry of the solution, we might assume that r~1 =r~2 =r, θ~1 =θ, θ~2 =π −θ and θ∈[0,π 2]. Then we can evaluate the integration in (80) as
)
Repeatedly substituting (C.13) into (C.12) to reduce the power of term r from 2 to 1 and using the trigonometric property 2sin2( ) + cos(2 ) = 1 can give
then substituting (C.15) into (C.14) yields (81). Similarly, by repeatedly substituting (C.12) and using the trigonometric property 2sin2( ) + cos(2 ) = 1, we can derive (C.11) as
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VITA
Han-Wen Hsu was born in Tainan, Taiwan in Oct. 1977. He received his B.S. degree from the Division of Applied Mathematics, the Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan in June 2000. He received his M.S. degree from the Department of Computer Science and Information Engineering, National Chiao Tung University, Hsinchu, Taiwan in June 2004, where he is currently working toward a Ph. D. degree in Computer Science and Engineering. His research interests are in audio coding and signal processing.
PUBLICATION LIST
Journal Papers
1. C.M. Liu, H.W. Hsu, and W.C. Lee, “Compression artifacts in perceptual audio coding,” IEEE Trans. Audio Speech Lang. Process., vol. 16, no. 4, pp. 681-695, May 2008.
2. H.W. Hsu and C.M. Liu, “Fast radix-q and mixed-radix algorithms for type-IV DCT,”
IEEE Signal Process. Lett., vol. 15, pp.910-913, Dec. 2008.
3. H.W. Hsu and C.M. Liu, “Autoregressive modeling of temporal/spectral envelopes with finite-length discrete trigonometric transforms,” Accepted with minor revisions, IEEE Trans. Signal Process., 2010.
4. H.W. Hsu and C.M. Liu, “Decimation-whitening filter in spectral band replication,”
submit to IEEE Trans. Audio Speech Lang. Process., 2010.
Conference Papers
1. D.P. Chen, H.F. Hsiao, H.W. Hsu, and C.M. Liu, “Gram-Schmidt-based downmixer and decorrelator in the MPEG Surround Coding,” appear to Proc. AES 128th Conv., London, UK, May 22–25, 2010.
2. C. M. Liu, H. W. Hsu, Y. H. Kao, and W. C. Lee, “Spatial parameter decision by least squared error in Parametric Stereo Coding and MPEG Surround,” in Proc. AES 126th Conv., Munich, Germany, May 7–10, 2009, preprint 7731.
3. C.M. Liu, H.W. Hsu, C.H. Yang, and W.C. Lee, “Low-power MPEG-4 HE-AAC version-2 encoder,” in Proc. AES 124th Conv., Amsterdam, Netherlands, May 17–20, 2008, preprint 7338.
4. C.M. Liu, C.H. Yang, H.W. Hsu, and W.C. Lee, “Design of framing in MPEG Surround based on dynamic programming algorithm,” in Proc. AES 124th Conv., Amsterdam, Netherlands, May 17–20, 2008, preprint 7487.
5. H.W. Hsu, C.L Hu, C.M Liu, and W.C. Lee, “On the design of low power MPEG-4 HE-AAC encoders,” in Proc. AES 122nd Conv., Vienna, Austria, May 5–8, 2007, preprint 6999.
6. H.W. Hsu, H.Y. Tseng, C.M Liu, W.C. Lee, and C. H. Yang, “High quality, low power QMF bank design for SBR, Parametric Coding, and MPEG Surround decoders,” in Proc.
AES 122nd Conv., Vienna, Austria, May 5–8, 2007, preprint 7000.
7. C.H. Yang, C. M. Liu, H.W. Hsu, K.C. Lee, S.H. Tang, Y.C. Yang, C.M. Chang, and W.C.
Lee, “Design of HE-AAC version 2 encoder,” in Proc. AES 121st Conv., San Francisco, USA, October 5–8, 2006, preprint 6873.
8. H.W. Hsu, C.M. Liu, and W.C. Lee, “Fast complex quadrature mirror filterbanks for
MPEG-4 HE-AAC,” in Proc. AES 121st Conv., San Francisco, USA, October 5–8, 2006, preprint 6871.
9. C. M. Liu, H. W. Hsu, C. H. Yang, K. C. Lee, S. H. Tang, Y. C. Yang, and W. C. Lee,
“Compression artifacts in perceptual audio coding,” in Proc. AES 121st Conv., San Francisco, USA, October 5–8, 2006, preprint 6872.
10. H.W Hsu, Y.C Yang, C.M. Liu, and W.C Lee, “ Design for high frequency adjustment module in MPEG-4 HEAAC encoder based on linear prediction method,” in Proc.
AES120th Conv., Paris, France, May 20–23, 2006, preprint 6755.
11. K.C. Lee, C.H. Yang, H.W. Hsu, W.C. Lee, C.M. Liu, and T.W. Chang, “Efficient design of time-frequency stereo parameter sets for parametric HE-AAC,” in Proc. AES 119th Conv., New York, USA, October 7–10, 2005, preprint 6600.
12. C.M. Liu, L.W. Chen, H.W. Hsu, and W.C. Lee, “Bit reservoir design for HE-AAC,” in Proc. AES 118th Conv., Barcelona, Spain, May 28-31, 2005, preprint 6382.
13. C.M. Liu, W.C. Lee, C.H. Yang, K.Y. Peng, T. Chiou, T.W. Chang, Y.H. Hsiao, H.W.
Hsu, and C.T. Chien, “Design of MPEG-4 AAC encoders,” in Proc. AES 117th Conv., San Francisco, USA, Oct. 28-31, 2004, preprint 6201.
14. H.W. Hsu, C.M. Liu, W.C. Lee, and Z.W. Li, “Audio patch method in MPEG-4 HE AAC decoder,” in Proc. AES 117th Conv., San Francisco, USA, Oct. 28-31, 2004, preprint 6221.
15. H. W. Hsu, C. M. Liu, and W. C. Lee, “Audio patch method in audio decoders—MP3 and AAC,” in Proc. AES 116th Conv., Berlin, Germany, May 8-11, 2004, preprint 6014.
16. C. M. Liu, W. C. Lee, and H. W. Hsu, “High frequency reconstruction for band-limited audio signal,” in Proc. the 6th Int. Conf. Digital Audio Effects (DAFX-03), University of London, September 8-11, 2003.
17. C. M. Liu, W. C. Lee, and H. W. Hsu, “High frequency reconstruction by linear extrapolation”, in Proc. AES115th Conv., New York, USA, Oct. 10-13, 2003, preprint 5968.