本文選題：時(shí)頻分析　切入點(diǎn)：多項(xiàng)式Chirplet變換　出處：《西安電子科技大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：瞬時(shí)頻率是時(shí)頻模式中的一種基本的參數(shù),在調(diào)頻信號(hào)中作為一個(gè)重要的角色,它已經(jīng)出現(xiàn)在雷達(dá)、檢測(cè)、語(yǔ)音等各個(gè)領(lǐng)域并獲得廣泛的應(yīng)用。研究瞬時(shí)頻率估計(jì)的方法以及相應(yīng)的參數(shù)估計(jì)在信號(hào)的時(shí)頻分析中具有重要的實(shí)用價(jià)值,而且時(shí)頻分布作為非平穩(wěn)信號(hào)的度量工具,它可以充分地展現(xiàn)出信號(hào)頻率隨著時(shí)間變化的規(guī)律,以及能夠在時(shí)頻分布中觀測(cè)到信號(hào)能量集中的程度。本文首要講述了瞬時(shí)頻率的基礎(chǔ)研究背景以及相應(yīng)各個(gè)概念產(chǎn)生的緣由,進(jìn)而定義了瞬時(shí)頻率普遍運(yùn)用的概念。其次又介紹了在時(shí)頻分析中常用的時(shí)頻分析方法：首先著重介紹了短時(shí)傅里葉變換以及Wigner-Ville分布,然而這兩種方法都存在各自的缺陷,并不能達(dá)到本文期望的效果,即在得到高度信號(hào)能量以及聚集性的同時(shí),估計(jì)的信號(hào)瞬時(shí)頻率更接近理論值。并由此引出了不同于以往的參數(shù)化時(shí)頻分析方法,其中詳細(xì)介紹了線性調(diào)頻小波變換和多項(xiàng)式線性調(diào)頻小波變換的算法實(shí)現(xiàn),并著重闡述了參數(shù)的選擇對(duì)參數(shù)化時(shí)頻分析方法的重要性。線性調(diào)頻小波變換的方法引入頻率旋轉(zhuǎn)算子和平移算子的概念,以及通過(guò)一個(gè)額外的用線性調(diào)頻率參數(shù)描繪核函數(shù)來(lái)處理線性調(diào)頻信號(hào)。進(jìn)而通過(guò)擴(kuò)展其頻率平移算子與旋轉(zhuǎn)算子,以及改變其核函數(shù),最終主要介紹本文重點(diǎn)研究的針對(duì)非線性調(diào)頻信號(hào)的多項(xiàng)式Chirplet變換的基本原理。本文主要研究的對(duì)象是參數(shù)化時(shí)頻分析方法——多項(xiàng)式Chirplet變換在瞬時(shí)頻率估計(jì)及參數(shù)估計(jì)中的應(yīng)用,該方法的核心是將多項(xiàng)式核函數(shù)來(lái)替代線性調(diào)頻小波變換中的線性核函數(shù),非常適合非平穩(wěn)非線性調(diào)頻信號(hào)的處理。為了保證時(shí)頻分析的質(zhì)量,本文提出了一種基于目標(biāo)信號(hào)的迭代算法自適應(yīng)選擇多項(xiàng)式Chirplet變換參數(shù)。該算法利用雷尼熵來(lái)終止迭代,計(jì)算出每次迭代中時(shí)頻表示的雷尼熵,當(dāng)后一次迭代的雷尼熵大于前一次迭代,或雷尼熵一直減小到不明顯變化時(shí)終止迭代。此外,該算法中還運(yùn)用到多項(xiàng)式擬合的方法去更好的匹配理論值,可以更好的估計(jì)瞬時(shí)頻率以及參數(shù)。最后,本文通過(guò)不同的目標(biāo)信號(hào)來(lái)進(jìn)行仿真試驗(yàn),通過(guò)觀察和數(shù)據(jù)分析,以及在加噪的情況下與其對(duì)比的試驗(yàn)手段,證明了本文算法的有效性。在與其它估計(jì)方法對(duì)比,本文方法的實(shí)驗(yàn)效果較為理想。
[Abstract]:Instantaneous frequency is a basic parameter in time-frequency mode. As an important role in FM signal, it has already appeared in radar, detection, The methods of instantaneous frequency estimation and the corresponding parameter estimation have important practical value in time-frequency analysis of signals, and time-frequency distribution is used as a measurement tool for non-stationary signals. It can fully show the variation of signal frequency over time. And the degree of signal energy concentration can be observed in time-frequency distribution. This paper mainly describes the basic research background of instantaneous frequency and the origin of the corresponding concepts. Then the concept of universal use of instantaneous frequency is defined. Secondly, the time-frequency analysis methods commonly used in time-frequency analysis are introduced. First, the short-time Fourier transform and Wigner-Ville distribution are introduced emphatically. However, each of these two methods has their own defects. It can not reach the desired effect in this paper, that is, the estimated instantaneous frequency of the signal is closer to the theoretical value, and the parameterized time-frequency analysis method is different from the previous method. The algorithms of LFM wavelet transform and polynomial LFM wavelet transform are introduced in detail. The importance of parameter selection to parameterized time-frequency analysis is emphasized. The concepts of frequency rotation operator and translation operator are introduced into the method of linear frequency modulation wavelet transform. And the LFM signal is processed by an extra description of the kernel function with linear frequency modulation parameters, and then by extending its frequency translation operator and rotation operator, and changing its kernel function, Finally, the basic principle of polynomial Chirplet transform for nonlinear frequency modulation signal is introduced. The main object of this paper is the parametric time-frequency analysis method-polynomial Chirplet transform in instantaneous frequency estimation and parameter. Applications in number estimation, The core of this method is to replace the linear kernel function in the linear frequency modulation wavelet transform with polynomial kernel function, which is very suitable for the processing of nonstationary nonlinear frequency modulation signals. In this paper, an iterative algorithm based on target signal is proposed to adaptively select polynomial Chirplet transform parameters. In this algorithm, Rayney entropy is used to terminate the iteration, and the Rayney entropy of time-frequency representation in each iteration is calculated. When the reni entropy of the last iteration is larger than that of the previous iteration, or if the Rayney entropy decreases until the change is not obvious, the iteration is terminated. In addition, the polynomial fitting method is used in the algorithm to better match the theoretical values. The instantaneous frequency and parameters can be better estimated. Finally, this paper carries out simulation experiments through different target signals, through observation and data analysis, as well as the test means compared with them in the case of adding noise. The effectiveness of the proposed method is proved. Compared with other estimation methods, the experimental results of this method are satisfactory.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.23

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