請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/74666
標題: | 時頻重新分布法在高階同步擠壓轉換下之改良 Improved Time-Frequency Reassignment Algorithm Using High-Order Synchrosqueezing Transforms |
作者: | De-Yan Lu 盧德晏 |
指導教授: | 丁建均 |
關鍵字: | 短時傅立葉轉換,連續小波轉換,時頻重新分布法,同步擠壓轉換,高階同步擠壓轉換, short-time Fourier transform (STFT),continuous wavelet transform (CWT),reassignment method (RM),sychrosqueezing transform (SST),high-order sychrosqueezing transform, |
出版年 : | 2020 |
學位: | 碩士 |
摘要: | 對於信號處理來說,時頻分析是一項非常重要的工具,它可以將一個時變信號展開成時間對頻域的關係,藉由此關係我們可以得知這個信號在某個時間點上的頻率是什麼,因此在應用方面其實非常多,像是聲音訊號、音樂信號、地震波等生活應用。在這篇碩士論文中,我們將對兩種信號做時頻分析。第一項是對純弦波和啁啾信號作分析、第二項是對聲音訊號來做分析。而我們會利用近期來的時頻分析方法來解析這些訊號。
傳統的時頻分析方法像是短時距傅立葉轉換、小波轉換等,可是我們都知道這類的時頻分析方法會受限於海森堡測不準原理的影響,造成在時間上的解析度和頻率上的解析度無法同時達到精準結果。因此,約在西元2000年左右衍生出新的時頻分析方法,名為重新分布法,重新分布法是根據時頻分析圖上的亮帶區域對其取重心,也就是將亮帶範圍重新移動至重心部分,可同時提高時間和頻率解析度部分,但缺點為它是不可逆的過程,能測試一個時頻分析方法的好壞就是它還原成原信號時會不會易受雜訊的影響,也稱作對雜訊的韌性程度。因此,近期來發展出一套新的時頻分析方 法,稱作同步擠壓轉換,同步擠壓轉換將頻率部分進行單方向位移,不像重新分布法是對頻率和時間同時進行位移,單方向位移的好處就是可逆,因此同步擠壓轉換是可逆的,但缺點就是它只是用於對於頻率對時間變化較不敏感的信號。因此發展出二階的同步擠壓轉換、甚至到高階的同步擠壓轉換。但是越高階其運算量越大,因此我們會有一個極限值,也就是約略估計到第幾階時就可停止運算。 而我們知道時頻分析常應用於信號上的處理,第一種我們應用的信號是純弦波和啁啾信號來做測試,來看說這兩種信號會不會有相互影響的Crossed terms的問題和解析度如何;第二種我們要應用的信號是聲音信號,我們都知道聲音信號上的處理是非常重要,對於我們萃取出來的信號以時頻分析方法進行了解,可以知道一個聲音信號到底有沒有倍頻成分,還有頻率對時間的關係如何變化,對於聲音信號上的處理這是一個非常重要的步驟,因此我們將使用好的時頻分析方法來使得解析度更為清楚。 For signal processing, time-frequency analysis is a very important tool. It can represent the signal in the time-frequency domain. With the representation, we can know what the instantaneous frequency is at certain time. Therefore, there are many applications in time-frequency analysis, such as sound, music, seismic, etc. In the conventional time-frequency method, we use the short-time Fourier transform(STFT) and the continuous wavelet transform(CWT) to analyze signals. However, the STFT and the CWT are limited by the Heisenberg Uncertainty principle, causing poor frequency resolution or poor time resolution. Therefore, some researchers generated a new method of time-frequency analysis about 2000, known as the reassignment method (RM). The RM calculates the center of gravity for the energy-band of time-frequency plane; i.e. it reassigns the energy-band to the center of gravity, which can improve the time and the frequency resolution simultaneously. However, the disadvantage of the RM is that it is not invertible. This implies that we cannot test robustness if we add noise to the signals. So, reconstruction is very important index for time-frequency method. Therefore, some researchers suggested a new time-frequency method for the ability of reconstruction, known as the sychrosqueezing transform (SST). The SST shifts the energy-band along the frequency axis, but the RM shifts the energy-band along the time axis and the frequency axis simultaneously. The advantage of the single direction is invertible for signal reconstruction. So, SST is invertible for signal reconstruction. However, it is only appropriate to the signals whose instantaneous frequency varies slowly with time. Thus, some researchers developed not only the second-order SST in 2013 but also the high-order SST in 2017. However, the complexity is very large when using the high-order SST. Thus, we have a threshold value when we run the high-order SST iteration; i.e. we can stop calculation at certain threshold value. We know that time-frequency analysis is often applied into signal processing. The first type of signals are pure sinusoid and chirps. We test them to observe if they have cross terms with each other and how the resolution is. And the second one is sound. We all know signal processing is very important for sounds. For the signals extracted by the time-frequency approach, we can know whether there are multiple frequency components and how the frequency varies with time by time frequency analysis in this thesis. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/74666 |
DOI: | 10.6342/NTU202000040 |
全文授權: | 有償授權 |
顯示於系所單位: | 電信工程學研究所 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
ntu-109-1.pdf 目前未授權公開取用 | 30.03 MB | Adobe PDF |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。