本論文研究一個麥克風陣列之波束成形系統，差分麥克風陣列擁有體積小、高指向性及與頻率無關的波束圖形等優點，在語音增強的應用中很有潛力，但是差分麥克風陣列有放大白雜訊的問題，抵銷語音增強上的優勢，造成輸出結果不如預期，尤其在高階的差分麥克風陣列越容易發生。
本論文提出譜減法之差分麥克風陣列，在訊號端方面使用譜減法，消除電子原件互相干擾產生的白雜訊，增加輸入訊號的訊雜比；差分麥克風陣列演算法方面，由於傳統時域差分麥克風陣列有設計靈活度低且白雜訊增益低等缺點，因此時頻域差分麥克風陣列架構較多數人使用，此架構的特色將時域訊號透過短時距傅立葉轉到時頻域，透過設計好的濾波器係數，達成保留特定方放的聲音、消除周遭環境音的效果，並且提升白雜訊增益。在時頻域差分麥克風的基礎上，設計一個強健性時頻域差分麥克風陣列，更有效地增加白雜訊增益。

This thesis studies a differential microphone array beamforming system. The differential microphone array has the advantages of small size, high directivity, and frequency-independent beampattern. It has great potential in speech enhancement applications. However, the differential microphone array suffers from a white noise amplification problem, which caused the output not as expected, especially in higher order differential microphone arrays.
In this thesis, a differential microphone array with spectral subtraction is proposed. The spectral subtraction method is used in the signal end to eliminate the white noise generated by the mutual interference of electronic components and increase the signal-to-noise ratio of the input signal. The time domain differential microphone array algorithm has low design flexibility and low white noise gain problem. Therefore, the time-frequency domain differential microphone array architecture is often used by many people. The feature of this architecture transforms the time domain signal to the time-frequency domain through the short-time Fourier transform and uses the designed filter coefficient to preserve the sound of a specific direction, eliminate the surrounding ambient sound, and increase the white noise gain. Based on the time-frequency domain differential microphone, a robust time-frequency domain differential microphone array is designed to increase the white noise gain more effectively.

[1] Hung-Ping Liu, Yu Tsao, and Chiou-Shann Fuh, “Bone-conducted speech enhancement using deep denoising autoencoder,” Speech Communization, vol. 104, pp. 106-112, Nov. 2018.
[2] Szu-Wei Fu, Tao-Wei Wang, Yu Tsao, Xugang Lu, and Hisashi Kawai, “End-to-End Waveform Utterance Enhancement for Direct Evaluation Metrics Optimization by Fully Convolution Neural Networks,” IEEE Trans. Audio, Speech, Lang. Process., vol. 26, no. 9, Sep. 2018.
[3] Xugang Lu, Yu Tsao, Shigeki Matsuda and Chiori Hori, “Speech Enhancement Based on Deep Denoising Autoencoder, ” in Proc. Interspeech, pp. 436-440, August 2013.
[4] STEVEN F. BoLL, “Suppression of Acoustic Noise in Speech Using Spectral Subtraction, ” IEEE Trans. Audio, Speech, Lang. Process., vol. ASSP-27, no. 2, Apr. 1979.
[5] M. Berouti, R. Schwartz, and J. Makhoul, “Enhancement of speech corrupted by acoustic noise,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, pp. 208-211, Apr. 1979.
[6] Wiener Norbert, Extrapolation Interpolation and Smoothing of Stationary Time Series, New York: Wiley, 1949
[7] R. Martin, “Noise power spectral density estimation based on optimal smoothing and minimum statistics,” IEEE Trans. Speech, Audio. Process., vol. 9, no. 5, Jul. 2001.
[8] Jalal Taghia, Rainer Martin, “A Frequency-Domain Adaptive Line Enhancer With Step-Size Control Based on Mutual Information for Harmonic Noise Reduction,” IEEE/ACM Trans. Audio, Speech, Lang. Process., vol. 24, no. 6, Jun. 2016.
[9] Yi Hu, P.C. Loizou, “Speech enhancement based on wavelet thresholding the multitaper spectrum,” IEEE Trans. Speech, Audio. Process., vol. 12, no. 1, Jan. 2014.
[10] E. De Sena, H. Hacihabiboğlu and Z Cvetković, “On the Design and Implementation of Higher Order Differential Microphones,” IEEE Trans. Audio, Speech, Lang. Process., vol. 20, pp. 162-174, Jan. 2012.
[11] J. Chen and J. Benesty, “A general approach to the design and implementation of linear differential microphone arrays,” in Proc. Asia-Pa-cific Signal Inf. Process. Assoc. Annu. Summit Conf.(APSIPA), 2013.
[12] Hao Zhang, Jingdong chen, Jacob Benesty, “Study of nonuniform linear differential microphone arrays with the minimum-form filter,” Appl. Acoust., vol. 98, pp. 62-69, Nov. 2015.
[13] C. Pan, J. Chen and J. Benesty, “Theoretical Analysis of Differential Microphone Array Beamforming and an Improved Solution,” IEEE/ACM Trans. Audio, Speech, Lang. Process., vol. 23, pp. 2093-2105, Nov. 2015.
[14] Liheng Zhao, Jacob Benesty, and Jingdong Chen, “Design of Robust Differential Microphone Arrays,” IEEE/ACM Trans. Audio, Speech, Lang. Process., vol. 22, no. 10, Oct. 2014.
[15] Liheng Zhao, Jacob Benesty, and Jingdong Chen, “Design of robust differential microphone arrays with the Jacobi-Anger expansion,” Appl. Acoust., vol. 110, pp. 194-206, Sep. 2016.
[16] Gongping Huang, Jacob Benesty, Jingdong Chen, “Superdirective Beamforming Based on the Krylov Matrix,” IEEE/ACM Trans. Audio, Speech, Lang. Process., vol. 24, no. 12, Dec. 2016.
[17] Xianghui Wang, Jacob Benesty, Israel Cohen, and Jingdong Chen, “Microphone array beamforming based on maximization of the front-to-back ratio,” J. Acoust. Soc. Amer. 144, 3450, Dec. 2018.
[18] Don H. Johnson, Dan E. Dudgeon, Array signal processing : concepts and techniques, Upper Saddle River, N.J: P T R Prentice Hall, 1993.
[19] O. L. Frost III, “An algorithm for linearly constrained adaptive beamforming,” Proc. IEEE, vol. 60, pp. 926-935, Aug. 1972.
[20] L. J. Griffiths and G. W. Jim, “Alternative approach to linear constrained adaptive beamforming,” IEEE Trans. Antennas Propagat., vol. AP-30, pp. 27-34, Jan. 1982.
[21] G. Elko and A. Pong, “A simple adaptive first-order differential microphone,” in Proc. IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, pp. 169-172, Oct. 1995.
[22] T. D. Abhayapala and A. Gupta, “Higher order differential-integral microphone arrays,” J. Acoust. Soc. Amer., vol. 127, no. 5, pp. EL227–EL233, Apr. 2010.
[23] A. Benardini, F. Antonacci and A. Sarti, “Wave Digital Implementation of Robust First-Order Differential Microphone Arrays,” IEEE Signal Processing Letters, vol. 25, Feb. 2018
[24] T.I. Laakso, V. Välimäki, M. Karjalainen, and U.K. Laine, “Splitting the unit delay,” IEEE Signal Process. Mag., vol. 13, no. 1, pp.30-60, Jan. 1996.
[25] M.A. Al-Alaoui, “Novel digital integrator and differentiator,” Electron. Lett., vol. 29, no. 4, pp. 376-378, Feb. 1993.
[26] J. Chen, J. Benesty, and C. Pan, “On the design and implementation of linear differential microphone arrays,” J. Acoust., Soc. Amer., vol. 136, pp. 3097-3113, Dec. 2014.
[27] J. Benesty, M. M. Sondhi, and Y. Huang, eds., Springer Handbook of Speech Processing. Berlin, Germany: Springer-Verlag, 2007.
[28] N. Stefanakis and D. Pavlidi, “Perpendicular Cross-Spectra Fusion for Sound Source Localization With a Planar Microphone Array,” IEEE Trans. Audio, Speech, Lang. Process., vol. 25, pp. 1821-1835, Sep. 2017.
[29] M. M. Faraji, S. B. Shouraki and E. Iranmehr, “Spiking Neural Network for Sound localization Using Microphone Array,” 23rd Iranian Conference on Electrical Engineering, pp. 1260-1265, Tehranm, Iran, May 2015.
[30] Matthew B. Hawes and Wei Liu, “Sparse Array Design for Wideband Beamforming With Reduced Complexity in Tapped Delay-Lines,” IEEE Trans. Audio, Speech, Lang. Process., vol. 22, pp. 1236-1247, Aug. 2014.
[31] J. Dmochowski, J. Benesty, and S. Affes, “On Spatial Aliasing in Microphone Arrays,” IEEE Trans. Signal Process., vol. 57, pp. 1383-1395, Apr. 2009.
[32] Y. Huang and J. Benesty, “A class of frequency-domain adaptive approaches to blind multi-channel identification,” IEEE Trans. Signal Process., vol. 51, pp. 11-24, Jan. 2003.
[33] M. Brandstein, and D. Ward, eds., Microphone Arrays: Signal Processing Techniques and Applications, Berlin, Germany: Springer-Verlag, 2001.
[34] Changlei Li, Jacob Benesty, and Jingdong Chen, “Beamforming based on null-steering with small spacing linear microphone arrays,” J. Acoust. Soc. Amer. 143, 2651, May 2018.
[35] Chao Pan, Jacob Benesty, and Jingdong Chen, “Design of robust differential microphone arrays with orthogonal polynomials,” J. Acoust. Soc. Amer. 138(2), 1079-1089, August 2015.
[36] Yaakov Buchris, Israel Cohen, Jacob Benesty, “On the design of time-domain differential microphone arrays,” Appl. Acoust., vol. 148, pp. 212-222, May 2019.
[37] Reuven Berkun, Israel Cohen, Jacob Benesty, “Combined Beamformers for Robust Broadband Regularized Superdirective Beamforming,” IEEE Trans. Audio, Speech, Lang. Process., vol. 23, No. 5, May 2015.
[38] Edwin Mabande, Adrian Schad, Walter Kellermann, “Design of robust superdirective beamforemrs as a convex optimization problem,” in Proc. IEEE Int. Conf. Acoust. Speech, Signal Process. (ICASSP-09), Taipei, Taiwan, pp. 77-80, April 2009.
[39] Zhong-Hua Fu, “Relaxing nulls for robust differential microphone array in the STFT domain,” 2017 International Conference on Orange Technologies(ICOT), 8-10, Dec. 2017.
[40] 王基鴻，「空間濾波器於麥克風陣列之設計」，國立中央大學電機工程學系，碩士論文，民國101年6月。
[41] 王冬霞，殷福亮，「聯合波束形成與譜減法的麥克風陣列語音加強算法」，大連理工大學學報，第46卷，第1期，2006年1月。