臺灣博碩士論文加值系統

小波轉換利用原型小波基底函數的擴展與收縮，在時間-比例平面上形成一組富有彈性的視窗，且在符合Constant-Q濾波原理之下，使得訊號之高、低頻率成份的解析皆有良好的效果。離散小波轉換更具有不少優點，例如它稀疏的取樣網格使得轉換更有效率，以及具區域化的基底函數則非常適於非穩態信號處理。而強健型離散小波轉換則使得離散小波轉換不但保存上述優點之外，更具有位移不變的特性。使得DWT在多重路徑的環境下，即多個信號成份各自有不同延遲時間時， 更有利於雷達或聲納的應用。
可適性密度估測亦可用來偵測瞬時信號， 偵測對象可為水下聲音，如鯨、海豚響聲等。響聲信號經小波拆解並予以整合後，利用整合資料之聯合分佈的遞迴密度估測進行信號偵測工作。在遞迴過程中，任何有別於此可適性密度估測者，即視為最具可能性的瞬時信號。
本論文即將強健型離散小波轉換應用到可適性密度估測，以期達到在多重路徑及水下背景環境噪音中，以偵測出信號的存在。

Wavelet transform is one way which utilizes dilation and contraction of prototype wavelet basis function, and forming a set of windows which is full of flexibility on the time--scale plane. Its filtering effect in the frequency domain does agree the constant--Q theorem and it has a good effect on the analysis of high or low component of signal. The discrete wavelet transform (DWT) is attractive for many reasons. Its sparse sampling grid eliminates redundancy and is very efficient. Its localized basis functions are well suited for processing non--stationary signals such as transients. Robust discrete wavelet transform (RDWT) provides a solution to the translation invariance problem while maintaining its other attractive attributes. Its translation
invariant properity suits applications such as radar and sonar, particularly in a multipath environment where numerous signal components arrive with arbitrary delays.
We consider the use of adaptive density estimation to a common signal processing, that of detecting transient features in sound recordings that contain interference. In this particular case, the data are obtained from various types of underwater sounds. Using recursive density estimation of the joint distrbution of certain summary features of its wavelet decomposition, we utilize an adaptive density estimation of the ackground interference. The observations considered to be outliers from this density estimate at any time are then flagged as potential"signals".
This thesis intends to apply the robust discrete wavelet transform to adaptive density estimation in order to detect signals in a multipath environment and to detect intermittent departures (potential"signals") from the background sound environment.

第一章 緒論
1.1 簡介與研究動機
1.2 相關研究與國內外研究情形
1.3 各章節之內容概要
第二章 小波概論
2.1 從傅氏分析看小波分析
2.2 積分小波轉換與時頻分析
2.3 反求式與對偶函數
2.4 多解析分析
第三章 多解析空間與信號空間
3.1 多解析空間
3.1.1 比例函數
3.1.2 小波函數
3.1.3 比例函數的特性
3.1.4 小波的特性
3.1.5 比例函數的生成
3.2 有限支持之正規小波參數化
3.2.1 正規小波
3.2.1 正規小波參數化
3.2.1 參數化設計實例
3.3 隨機程序之動量估測
3.3.1 平均值與相關函數之估計
3.3.2 相關矩陣之估計
3.4 離散 Karhunen-Loeve 轉換
3.4.1 DKLT介紹
3.4.2 DKLT之最佳化表示式
第四章 強健型離散小波轉換
4.1 子空間位移不變性
4.1.1 多路徑信號之偵測
4.1.2 離散小波轉換
4.1.3 可位移性之定義
4.2 位移誤差之比較
4.2.1 Zak轉換
4.2.2 位移誤差
4.2.3 能量分佈密度函數ESD
4.3 位移不變之比例函數的製作
4.3.1 整型演算法
4.3.2 位移不變之比例函數
4.3.3 整型演算法於db3位移不變之比例函數製作
第五章 強健型離散小波轉換於可適性密度估測之應用
5.1 信號於多路徑干擾下的偵測
5.1.1 多路徑干擾
5.1.2 多路徑干擾之偵測模擬
5.2 可適性密度估測
5.2.1 離散小波轉換
5.2.2 小波拆解與信號偵測
5.2.3 可適性密度估測
5.3 強健型離散小波轉換於可適性密度估測之應用
第六章 結論及未來研究方向
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