丁建均Ding, Jian-Jiun臺灣大學:電信工程學研究所王文阜Wang, Wen-FuWen-FuWang2010-07-012018-07-052010-07-012018-07-052009U0001-0206200913444200http://ntur.lib.ntu.edu.tw//handle/246246/188312傅立葉轉換是傳統上很常用來分析頻率的工具，不過它卻不能使用在非穏態訊號上。所以傅立葉轉換只適合用於穏態訊號且線性訊號。因此有了時頻域分佈函數針對非穩態訊號且線性訊號的分析工具。時頻分析的理論發展至今，已為訊號分析領域帶來極為深遠的影響，其運用範圍十分廣泛，涵蓋了語音、物理、心電圖、地球科學、音樂。為了得到訊號的時變頻譜特性，許多學者提出了各種形式的時頻分析函數，例如：短時間傅立葉轉換（STFT）、韋格納（WD）、加伯（GT），各種分佈多達幾十種。 本篇論文主要分成三個部份：第一部份為時頻分析，包括了各種時頻分析的理論介紹，及其優缺點比較、模擬結果，應用範圍等。更提出多種方法降低時頻分析在實作上的運算量。二部份特別介紹希爾伯－黃轉換（HHT），黃鍔院士於1998年發表提出。有別於傳統的時頻分析方法，傳統的方法是不夠的，因為它們均必須假設訊號為線性。因此，介紹了適合用於非穩態訊號且非線性訊號的分析工具。 第三部份為時頻分析與隨機程序的關係，我們研究發現各種時頻分析的方法與隨機程序有著定理的關係存在。The Fourier transform is an important tool in frequency analysis, but it cannot use for non-stationary or time-varying signals. Since The Fourier transform only deal with the stationary and linear signals. The time-frequency distribution function deals with the non-stationary and linear signals. It describes signals in terms of joint time-frequency form and is a powerful tool for analyzing signals. It has been widely applied in much kind of fields, such as speech, physics, electrocardiography (ECG), earth science and music. It is particularly useful for people to analyze signals with continuously time-varying frequency way. A lot of the time-frequency analysis have been widely used and researched for a number of years, such as the short time Fourier transform, the Wigner distribution, the Gabor transform, and other distributions. This thesis mainly has three parts: The first part is the time-frequency analysis. We will introduce a lot of algorithm of the time-frequency distribution, including the theorem of algorithms, advantages and disadvantages, simulations, and applications. We will propose some fast implementation algorithms to reduce the computation. The second part will introduce a recently method, the Hilbert-Huang transform (HHT), by Huang (1998). Traditional data analysis methods are all based on linear and stationary assumptions. The HHT can to solve the problem that the data is non-linear and non-stationary.he third part we will discuss the relation between the random process (including the stationary and the non-stationary ones) and several well-known time-frequency distributions.口試委員會審定書 #謝 i文摘要 iiBSTRACT iiiONTENTS vIST OF FIGURES ixIST OF TABLES xivhapter 1 Introduction 1.1 Subject 1.2 Chapter Overview 1.3 Abbreviations 3hapter 2 Wigner Distribution 5.1 Wigner Distribution 5.2 Wigner Ville Distribution 7.3 Modified Wigner Distribution 8.4 Pseudo L-Wigner Distribution 9hapter 3 Gabor Transform 13.1 Short Time Fourier Transform 13.2 Gabor Transform 16.3 Spectrogram 19.4 S-Transform 20.4.1 The Original S-Transform 20.4.2 The Generalized S-Transform 22.4.3 Novel S-Transform with the Special Varying Window 22.4.4 Properties of S-Transform 24hapter 4 Other Important Time-Frequency Distributions 27.1 Cohen’s Class Time-Frequency Distribution 27.1.1 Ambiguity Function 27.1.2 The Choi-Williams Distribution 30.1.3 The Cone-Shape Distribution 32.1.4 The Page Distribution 34.2 Pei-Tsai Distribution 36.3 Gabor-Wigner Transform 40.4 Matching Pursuits 43hapter 5 Hilbert-Huang Transform 45.1 Introduction 45.2 The Hilbert-Huang Transform 45.3 Instantaneous Frequency 46.4 Empirical Mode Decomposition (EMD) 48.4.1 Intrinsic Mode Functions (IMF) 48.4.2 The Sifting Process 50.4.3 Simulation of EMD 56.5 Hilbert Spectral Analysis (HSA) 60.6 Comparison and the Advantage of HHT 62.6.1 Comparison 62.6.2 Advantages of HHT 63.7 Summary 64hapter 6 Improvement of Time-Frequency Distributions 65.1 Down-Sampling for Time-Frequency Distribution 65.2 Complex the Input to Reduce Computation 68.3 Adaptive Time-Frequency Distribution 68.3.1 Simulation Results and Performance Comparison 71.4 Improvement the Pseudo L-Wigner Distribution 85.4.1 The Digital Implementation of Pseudo L-Wigner Distribution 85.4.2 Combination of MWD and PLWD 87.5 Fast Algorithm of the Gabor-Wigner Transform 89.6 Fast Algorithm of the Cohen’s Class Distribution 91.7 Fast Algorithm of the modified Wigner Distribution 92.8 Fast Algorithm of the S Transform 95hapter 7 Relations between Time-Frequency Distributions and Random Process 99.1 Introduction 99.2 Relations between Random Process and S Transform 101.3 Relations among Random Process, Spectrogram, and Modified Wigner Distribution Function 104.4 Relations among Random Process and Scalogram 108hapter 8 Conclusions and Future Work 111.1 Conclusions 111.2 Future Work 111EFERENCE 1132740114 bytesapplication/pdfen-US時頻分析短時間傅立葉轉換韋格納加伯希爾伯-黃轉換可適性時頻分析隨機程序傅立葉轉換time-frequency analysisshort time Fourier transformWigner distributionGabor transformHilbert Huang transformadaptive time-frequency distributionrandom processFourier transformthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/188312/1/ntu-98-R96942061-1.pdf