魏格納-韋立分佈具有高訊號解析度，但交關項干擾嚴重，而對高階非線性FM訊號也會有能量擴散效應；短時距傅立葉轉換無交關項干擾，但解析度卻不佳。因此提出多項式魏格納分佈及高階L魏格納分佈，以解決在線性和高階非線性FM訊號的能量擴散效應，並應用短時距傅立葉轉換之架構推導出修正型多項式魏格納分佈及修正型高階L魏格納分佈，除可保有高能量集中性並能有效消除交關項。雖然修正型演算法可提高魏格納-韋立分佈的訊號解析度，但由於修正型演算法的窗長度是固定的，因此無法適應不同類型訊號進行解析，造成解析度及抗雜訊能力受到限制，我們結合適應性演算法得到適應性高階L魏格納與適應性多項式魏格納分佈，使能在每個時間依訊號特性去調整窗長度，達到較佳解析效果並增強抗雜訊能力。另外亦修正短時距傅立葉轉換在每個時刻依時頻分佈函數所定義不明點平面的特性，設計最佳長度的核心函數，利用所得的最佳長度去調整短時距傅立葉轉換的窗長度，藉此提升短時距傅立葉轉換的解析度，達到適應性的短時距傅立葉轉換。
我們更將所發展的方法以LabVIEW數位信號處理軟體進行空氣實驗， 並由模擬與實驗結果，驗證所提方法之可行性與正確性。

The Wigner-Ville Distribution (WVD) has high resolution for monocomponent and linear FM Signals, but it has severe cross-term interference. The short-time Fourier Transform (STFT) dose not have cross-terms problem, but it has bad resolution. The polynomial WVD (PWVD) and higher order LWD are proposed to resolve the optimal energy concentration of WVD for processing higher order nonlinear FM signals. In order to avoid cross-term interference, we use STFT to established PWVD and LWD, and it results in modified PWVD and modified LWD. However, for noisy nonstationary signals, the modified algorithms still can not get high resolution. To enhance the performance of modified PWVD and modified LWD methods, the window length used in computation should be property selected according to the signal. These adaptive algorithms have better performace for nonstationary signal containated by noise. Furthermore, we introduced a technique to adaptively optimize the cone kernel distribution (CKD) for STFT by adjusting the cone length in response to changing signal. The resulting adaptive STFT shares many desirable properties with adaptive CKD and STFT.
Finally, the LabVIEW language is also used to implement the derived adaptive algorithm, and some experiments for nonstationary signals analysis using the adaptive algorithm are conducted.

第一章 緒論 1
1.1 簡介 .................................................................................................................................................... 1
1.2 相關研究文獻 .................................................................................................................................... 2
1.3 研究背景與動機 ................................................................................................................................ 3
1.4 本論文各章節要點概述 .................................................................................................................... 3
1.5 本論文專有名詞之縮寫 .................................................................................................................... 4
第二章 時頻分佈函數 ................................................................................................................................ 6
2.1 簡介 .................................................................................................................................................... 6
2.2 短時距傅利葉轉換 ............................................................................................................................ 7
2.3 小波轉換 ............................................................................................................................................ 9
2.4 魏格納-韋立分佈 ............................................................................................................................... 11
2.5 不明點函數 ........................................................................................................................................ 13
2.6 時頻分佈函數 ................................................................................................................................... 16
2.7 常見之時頻分佈函數 ....................................................................................................................... 17
2.8 時頻分佈函數之特性 ....................................................................................................................... 19
第三章 適應性多項式魏格納-韋立分佈 .................................................................................................. 23
3.1 簡介 .................................................................................................................................................... 23
3.2 多項式魏格納-韋立分佈 ................................................................................................................... 24
3.2.1 魏格納-韋立分佈 ............................................................................................................................ 25
3.2.2 多項式魏格納-韋立分佈 ................................................................................................................ 26
3.3 修正型L-魏格納分佈 ......................................................................................................................... 28
3.3.1 L-魏格納分佈 .................................................................................................................................. 28
3.3.2 假性L-魏格納分佈 .......................................................................................................................... 30
3.3.3 修正型L-魏格納分佈 ..................................................................................................................... 32
3.4 修正型多項式魏格納分佈 ................................................................................................................ 33
3.5 適應性高階L-魏格納 ......................................................................................................................... 35
3.6 適應性多項式魏格納分佈 ................................................................................................................ 38
3.7 電腦模擬 ............................................................................................................................................ 40
第四章 適應性短時距快速傅利葉轉換 ................................................................................................... 56
4.1 簡介 .................................................................................................................................................... 56
4.2 短時距傅利葉轉換 ............................................................................................................................ 57
4.3 即時遞迴演算法的分析 .................................................................................................................... 59
4.4 適應性錐形分佈函數 ........................................................................................................................ 61
4.4.1 短時距不明點函數 ......................................................................................................................... 62
4.4.2 錐形核心長度的最佳化 ................................................................................................................. 62
4.4.3 CKD即時處理的更新方程式 ......................................................................................................... 64
4.5 適應性短時距快速傅利葉轉換 ........................................................................................................ 65
4.6 電腦模擬 ............................................................................................................................................ 67
第五章 聲波訊號實驗 ............................................................................................................................... 76
5.1 簡介 .................................................................................................................................................... 76
5.2 LabVIEW簡介及實驗架構 ................................................................................................................ 76
5.3 實驗結果 ............................................................................................................................................ 77
5.3.1 合成聲波實驗 ................................................................................................................................. 78
5.3.2 聲音資料的辨識 ............................................................................................................................. 79
第六章 結論與未來發展方向 ................................................................................................................... 89
6.1 結論 .................................................................................................................................................... 89
6.2 未來發展方向 .................................................................................................................................... 90

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