可變視窗時頻域S轉換及群聚訊號分離法

本篇論文由四個主要的章節組成，在第二章節中，我們將介紹時頻分析的基本概念，一些比較常見的時頻分析以及它們的特性也會逐一的討論，例如：短時間傅利葉轉換和韋格納分布等等。除此之外，他們的優缺點以及一些取捨的問題也會在此處比較。在第三章節中，我們將討論S轉換，R. G. Stockwell et al. [6] 於1996年提出S轉換並認為此轉換是由短時間傅利葉轉換和小波轉換推導而來的，和S轉換相關的理論也會在此處做些說明，例如：TT-transform、時時濾波、時頻濾波。我們提出一個新的可變視窗，和原本S轉換不同的是此視窗可以依據訊號的性質來調整解析度，以取得更好的時頻分布圖。在第四章節中，我們提出計算DOST的快速演算法，由於IFFT的幫忙，我們可以比原來的計算方式快上好幾倍。一個新的少量戎餘離散S轉換將會在此提出，也會和原本的S轉換以及DOST做比較。在最後一章，我們將探討未知語音訊號分離的問題，我們針對已有的分群方法做修改，和原本方法不同之處在於在訊號分離之前我們使用了STFT時頻濾波以及不同的比重公式。和soft-LOST演算法相比較，我們的方法有更好的結果。

關鍵字

時頻分佈； S轉換；時頻濾波；離散正規正交S轉換；未知語音訊號分離法

並列摘要

There are four important chapters in this thesis. In chapter 2 we introduce the basic idea of time-frequency representation (TFR); some conventional TFRs, such as Short Time Fourier transform (STFT), Wigner distribution and etc., and their properties will be discussed respectively. Besides, we will also compare their major advantages, disadvantages, and some trade-off. The S-transform, a combination of STFT and Wavelet transform, proposed by R. G. Stockwell et al. in 1996 [6], will be illustrated in chapter 3. Some related topics, TT-transform, time-time filter, and time-frequency filter, will also be mentioned. We propose a novel window to adjust the time-frequency resolution of the original S-transform in order to get a better representation of the signal and do time-frequency filtering. We propose a fast algorithm for discrete orthonormal S-transform (DOST) in chapter 4, and due to the help of IFFT our new algorithm could run much faster than the original algorithm. A new modified discrete S-transform with less redundancies will be discussed here and compared with the original S-transform and DOST. In the final chapter, a modified clustering method for Blind Audio Source Separation will be proposed; our major contributions are the additional STFT time-frequency filtering before the source estimation and different weighting formula. Comparing the soft-LOST with our method, our method really does a better job.

並列關鍵字

time-frequency representation ； S-transform ； time-frequency filter ； discrete orthonormal S-transform ； blind audio source separation

參考文獻

[2] M. J. Bastiaans, “Gabor’s expansion of a signal into Gaussian elementary signals,” Proc. IEEE, vol. 68, pp. 594-598, 1980.

[3] L. Cohen and C. Lee, “Standard deviation of instantaneous frequency,” in Proc. IEEE ICASSP, 1989, pp. 2238–2241.

[5] F. Hlawatsch, G.F. Boudreaux-Bartels, “Linear and quadratic time-frequency signal representations”, IEEE Signal Proc. Mag., vol 9, April 1992. –P. 21-67.

[6] R. G. Stockwell, L. Mansinha, and R. P. Lowe, “Localization of the complex spectrum: the S transform,” IEEE Trans. Signal Process., vol. 44, no. 4, pp. 998–1001, Apr. 1996.

[7] McFadden, P. D., Cook, J. G., and Forster, L. M., 1999, “Decomposition of gear vibration signals by the generalised S-transform,” Mech. Syst. Signal Process., 13, 691–707.

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可變視窗時頻域S轉換及群聚訊號分離法

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