本論文內容將針對聲源訊號分離與聲場重建兩類問題，提出兩種創新的演算法。聲源訊號分離演算法是以時間反轉法為基礎，先利用摺積矩陣法求解場點與各聲源點間之脈衝響應函數，在藉由時間反轉其自適應聚焦特性，將場點之聲音訊號進行被動式時間反轉法之數位訊號處理，還原特定聲源位置之聲音訊號。由模擬及實驗結果得知，於無反射環境(自由聲場)下，時間反轉法與波束合成法具有相同的訊號分離效果。於反射環境下，時間反轉法則具有較好的訊號分離效果。並且當陣列之數量提升、間距或長度增加、量測距離縮短時，其訊號分離效果可獲得提升。
聲場重建演算法是以近似聲源法為基礎，先利用波束合成法對聲源進行定位，在以近似聲源法求解虛擬聲源強度，最後將所求得之虛擬聲源取代真實聲源，並重建聲場之聲壓分佈。由模擬及實驗結果得知，此演算法不受陣列間距需小於聲源波長的限制，並且改善了平面近似聲源法無法重建量測距離以內聲場的問題。由於兩種演算法均包含反矩陣的求解運算，為了抑制量測雜訊對反矩陣運算所造成的影響，本研究於反算過程中加入正規化法，避免在反算過程中因雜訊造成的發散問題。

In this paper, two innovation algorithms, which are the audio signal separation algorithm and the sound field reconstruction algorithm, are presented. The audio signal separation algorithm is based on the time-reversal method (TRM). The first step in this procedure is to calculate the impulse response function (IRF) between each source and field points by using deconvolution process. The second step in this procedure is to compute the passive time-reversal process on the signals of field points. Then, the signal of specific source can be separated via the self-adaptive focusing of time-reversal. The results for simulation and experiment indicate following conclusions, the performance of TRM is the same as that of beamforming when the environment is a non-reverberant field (free field). The performance of TRM is better than that of beamforming when the environment is a reverberant field. The performance of TRM can be enhanced by increasing the number of sensors, the spacing of array sensor or the length of array and decreasing the measuring distance.
The sound field reconstruction algorithm is based on the similar source method (SSM). The first step in this procedure is to search the source location by using beamforming approach. The second step in this procedure is to solve the source strength of virtual sources by using SSM. Finally, the sound pressure distribution of sound field can be reconstructed via the virtual sources, which have replaced the source. The results for simulation and experiment indicate following conclusions, the algorithm is not confined to a condition in which the measuring spacing must be smaller than wavelength of source. This algorithm can also reconstruct a sound field within measuring distance.
Furthermore, the Tikhonov regularization process is used to avoid the singularity effect from noise in deconvolution process and inverse calculation which are included in the two algorithms, respectively. Finally, several simulations and experimentations are shown to verify two innovation algorithms in the present study.

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