當我們處理具有相關性的訊號源時，使用傳統時域適應性限制性和非限制性最小均方值演算法，其收斂速度將會變得緩慢。因此，使得時間延遲估測的品質嚴重變差。為了改善這個問題，已有學者提出一種適應性限制性離散餘弦轉換最小均方值演算法解決。然而，任何正交轉換的使用將不對所有類型的訊號都能完全地把輸入訊號自相關矩陣對角化。事實上，在轉換域自相關矩陣中，重要的非對角元素將使得適應性限制性離散餘弦轉換最小均方值演算法的收斂品質變差。
為了進一步解決上述的問題，在本論文中，我們提出了適應性限制性修正式離散餘弦轉換最小均方值演算法來對所有類型的輸入訊號做時間延遲估測。除此之外，基於離散小波轉換的正交性，我們也提出了適應性限制性修正式離散小波轉換最小均方值演算法，並且把它應用在時間延遲估測的問題上。對於不同訊號源的類型而言，我們證明了這兩個提出的修正式限制性方法在時間延遲估測上，會得到較好的估測品質比使用非修正式的方法。此外，從模擬的結果，我們可以觀察出使用適應性限制性修正式離散餘弦轉換最小均方值演算法的估測品質稍微優於適應性限制性修正式離散小波轉換最小均方值演算法。

The convergence speed using the conventional approaches, viz., time-domain adaptive constrained and unconstrained LMS algorithms, becomes slowly, when dealing with the correlated source signals. In consequence, the performance of time delay estimation (TDE) will be degraded, dramatically. To improve this problem, the so-called transform-domain adaptive constrained filtering scheme, i.e., the adaptive constrained discrete-cosine-transform (DCT) LMS algorithm, has been proposed in [15]. However, the use of any one orthogonal transform will not result in a completely diagonal the input signal auto-correlation matrix for all types of input signals. In fact, the significant non-diagonal entries in the transform-domain auto-correlation matrix, will deteriorate the convergence performance of the algorithm.
To further overcome the problem described above, in this thesis, a modified approach, referred as the adaptive constrained modified DCT-LMS (CMDCT-LMS) algorithm, is devised for TDE under a wide class of input processes. In addition, based on the orthogonal discrete wavelet transform (DWT), an adaptive constrained modified DMT-LMS (CMDWT-LMS) algorithm is also devised and applied to the problem of TDE. We show that the proposed two modified constrained approaches for TDE does perform well than the unmodified approaches under different source signal models. Moreover, the adaptive CMDCT-LMS filtering algorithm does perform slightly better than the adaptive CMDWT-LMS filtering algorithm as observed from the simulation results.

Acknowlegement i
Abstract ii
Contents iii
List of Figures and Tables v
Chapter 1 Introduction 1
Chapter 2 Adaptive Constrained Modified DCT-LMS Filtering Algorithm
for Time Delay Estimation
2.1 Introduction 3
2.2 Conventional Adaptive Constrained DCT-LMS Filtering Algorithm for TDE 4
2.2.1 Statement of Signal Model for TDE 4
2.2.2 Adaptive Constrained DCT-LMS Filtering Algorithm for TDE 7
2.3 Adaptive Constrained Modified DCT-LMS Filtering Algorithm for TDE 11
2.4 Computer Simulation Results 13
Chapter 3 Adaptive Constrained Modified DWT-LMS Filtering Algorithm
for Time Delay Estimation
3.1 Introduction 24
3.2 Discrete Wavelet Transform 24
3.3 Adaptive Constrained Modified DWT-LMS Filtering Algorithm for TDE 32
3.4 Computer Simulation Results 36
Chapter 4 Conclusions 44
Appendix A 45
Appendix B 48
Appendix C 52
References 54

[1] Y. T. Chan, J. M. Riley and T.B. Plant, “A parameter estimation approach to time delay estimation and signal detection,” IEEE Trans. on Acoustics, Speech and Signal Processing, vol. ASSP-28 (1), pp. 8-16, February 1980.
[2] F. A. Reed, P. L. Feintuch, and N. J. Bershad, “Time delay estimation using the LMS adaptive filter-static behavior,” IEEE Trans. on Acoustics, Speech and Signal Processing, vol. ASSP-29 (3), pp. 561-571 June 1981.
[3] P. L. Feintuch, J. Bershad, and F. A. Reed. “Time delay estimation using the LMS adaptive filter-Dynamic behavior,” IEEE Trans. on Acoustics, Speech and Signal Processing, vol. ASSP-29 (3), pp. 571-576, June 1981.
[4] P.C. Ching and Y. T. Chan, “Adaptive time delay estimation with constraints,” IEEE Trans. on Acoustics, Speech and Signal Processing, vol. 36 no. 4, pp. 599-602, April 1988.
[5] S. N. Lin, and S. J. Chern, “A new adaptive constrained LMS time delay estimation algorithm,” Signal Processing, vol. 71(1), pp.29-44, April 1998.
[6] S. J. Chern, and S. N. Lin, “An adaptive time delay estimation with direct computation formula,” J. of Acoust. Soc. of Amer, 96 (2), pp. 811-820 March 1994.
[7] G. C. Carter, “Coherence and time delay estimation,” Proc. IEEE, vol. 75(2), pp.236-255, February 1987.
[8] B. Widrow and S.D. Stearns, Adaptive Signal Processing, Engle-wood Cliffs, NJ: Prentice-Hall, 1985.
[9] R. D. Gitlin and F. R. Magee, “Self-orthogonalizing adaptive equalization algorithms,” IEEE Trans. Commun., vol. COMM-25, pp. 666-672, July 1977.
[10] S. S. Narayan, A. M. Peterson and M. J. Narasimha, “Transform domain LMS algorithm,” IEEE Trans. on Acoustics, Speech and Signal Processing, vol. ASSP-31(3), pp. 609-615, June 1983.
[11] J. C. Lee, and C. K. Un, “Performance of transform-domain LMS adaptive digital filters,” IEEE Trans. on Acoustics, Speech and Signal Processing, vol. ASSP-34 (3), pp. 499-510, June 1986.
[12] D. F. Marshall, W. K. Jenkins, and J. J. Murphy, “The use of orthogonal transform for improving performance of adaptive filters,” IEEE Trans. on Circuits and Systems vol. 36(4), pp. 474-483, April 1989.
[13] F. Beaufays, “Transform-domain adaptive filters: An analysis approach,” IEEE Trans. on Signal Processing, vol. 43 (2), pp.422-431 February 1995.
[14] V. N. Parikh , and A. Z. Baraniecki, “The use of the modified Escalator algorithm to improve the performance of transform-domain LMS adaptive filters,” IEEE Trans. on Signal Processing, vol. 46 (3) , pp.625-635, March 1998.
[15] S. J. Chern, S. N. Lin and J. J. Jian, “Adaptive Constrained Transformed Domain Normalized LMS Time-Delay Estimation Algorithm,” Proc. of 2000 IEEE International Symposium on Intelligent Signal Processing and Communication Systems, Honolulu, Hawaii, U.S.A., B7-3-3, pp. 480-486, Nov. 2000.
[16] Haykin, S., Modern Filters. Macmillan Publishing Company, New York, U.S.A. 1989.
[17] Raghuveer M. Rao, Ajit S. Bopardikar, Wavelet transforms: introduction to theory and applications, Addison-Wesley, 1998.
[18] I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Comm. In Pure Applied Math, vol 41 no. 7, pp.909-996, 1988.
[19] I. Daubechies, Ten Lectures on Wavelets. New York: SIAM, 1992.
[20] Rioul, O.; Duhamel, P. “Fast algorithms for discrete and continuous wavelet transforms,” Information Theory, IEEE Trans., vol: 38 issue: 2 part: 2, pp. 569 –586, March 1992.
[21] Patrice Abry and Patrick Flandrin, “On the initialization of the discrete wavelet transform algorithm,” IEEE Signal Processing Letters, vol. 1 no. 2, pp.32-34, February 1994.
[22] I. Daubechies., “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inform. Theory, vol 36 , pp.961-1005, Sept 1990.
[23] Feng Liu, Jun Cheng, Jinbiao Xu, and Xinmei Wang, “Wavelet based adaptive equalization algorithm,” IEEE Proc.ICASSP , pp.1230-1234 1997.
[24] M. Doroslovacki, and Hong Fan, “Wavelet-based linear system modeling and adaptive filtering,” IEEE Trans. SP, vol.44, no.5, pp1156-1167 , May 1996.
[25] Hosur, S., Tewfik, A.H., “Wavelet transform domain LMS algorithm,” Acoustics, Speech, and Signal Processing, 1993. ICASSP-93., 1993 IEEE International Conference on , vol. 3 , pp.508 -510 1993.
[26] Nurgun Erdol, and Filiz Basbug, “Wavelet transform based adaptive filters: analysis and new results,” Signal Processing, IEEE Trans., vol.44 issue: 9, pp. 2163 –2171, Sept. 1996.
[27] Srinath Hosur , and Ahmed H. Tewfik, “Wavelet transform domain adaptive FIR filtering,” Signal Processing, IEEE Transactions on , vol. 45 issue: 3 , pp. 617 –630, March 1997.
[28] J. R. Treichler, “Transient and convergent behavior of the adaptive line enhancer,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-27(1) , pp.53-62, February 1979.
[29] Haykin. S., Adaptive Filter Theory, 3rd Ed. Prentice Hall, Englewood Cliffs, New Jersey, U.S.A. 1996.