本文選題：線性正則變換 + 二次調(diào)頻信號(hào)��； 參考：《北京理工大學(xué)》2014年博士論文

【摘要】：二次調(diào)頻信號(hào)是在自然界和工程技術(shù)領(lǐng)域中都有著廣泛存在的一種非平穩(wěn)信號(hào)，噪聲背景中二次調(diào)頻信號(hào)的時(shí)頻分析及參數(shù)估計(jì)是它在實(shí)際應(yīng)用中需要解決的共性問題。因此對二次調(diào)頻信號(hào)的檢測和參數(shù)估計(jì)問題進(jìn)行研究具有重要理論意義和實(shí)際應(yīng)用價(jià)值。 傳統(tǒng)的二次調(diào)頻信號(hào)參數(shù)估計(jì)算法主要通過高階次的非線性變換進(jìn)行降階，進(jìn)而使用已有的或構(gòu)造新的時(shí)頻分布估計(jì)參數(shù)。但這類算法的高階次非線性變換會(huì)帶來較高的信噪比門限和較低的輸出信噪比，或者運(yùn)算量較大。線性正則變換作為Fourier變換、分?jǐn)?shù)階Fourier變換的推廣形式，具有三個(gè)自由參數(shù)，因而靈活性更強(qiáng)，并且具有快速算法，故變換的運(yùn)算量較低。為豐富和發(fā)展線性正則變換的基礎(chǔ)理論和探討高性能的二次調(diào)頻信號(hào)參數(shù)估計(jì)算法，，本文結(jié)合線性正則變換在信號(hào)處理方面的優(yōu)勢和特點(diǎn)，構(gòu)造基于線性正則變換的新的時(shí)頻分布，研究它們的相關(guān)理論，并探討相關(guān)理論成果在二次調(diào)頻信號(hào)參數(shù)估計(jì)中的應(yīng)用。主要的貢獻(xiàn)及創(chuàng)新性成果如下： 1、為深入研究二次調(diào)頻信號(hào)參數(shù)估計(jì)問題，本文首先研究了線性正則變換的相關(guān)基礎(chǔ)理論。首先提出了基于線性正則變換的模糊函數(shù)，對它的相關(guān)特征性質(zhì)作了深入的分析和研究；進(jìn)一步考察了基于線性正則變換的模糊函數(shù)與其它時(shí)頻分析工具之間的關(guān)系，發(fā)現(xiàn)一些常用的時(shí)頻分布可以由基于線性正則變換的模糊函數(shù)來表示；給出了常見信號(hào)的基于線性正則變換的模糊函數(shù)。對于信號(hào)線性正則變換后的模糊函數(shù)，研究了它的卷積性、乘積性及相關(guān)性等特性。再次，提出基于線性正則變換的Wigner-Ville分布這一新的時(shí)頻分布，推導(dǎo)了它的一些新的重要性質(zhì)，研究了與其它時(shí)頻分析方法之間的關(guān)系，并對常見信號(hào)的基于線性正則變換的Wigner-Ville分布進(jìn)行了分析等。最后，針對二維線性正則變換，在給出它的一些常用性質(zhì)的基礎(chǔ)上，提出了二維線性正則域的卷積、乘積理論，并通過實(shí)例驗(yàn)證了二維線性正則變換的數(shù)值計(jì)算，分析了二維線性正則變換的運(yùn)算量。上述線性正則變換的基本理論的建立，一方面進(jìn)一步豐富了線性正則變換的理論體系，另一方面也為研究二次調(diào)頻信號(hào)的參數(shù)估計(jì)算法奠定了相關(guān)理論基礎(chǔ)。 2、提出了基于廣義線性正則變換的二次調(diào)頻信號(hào)參數(shù)估計(jì)算法。在線性正則變換的定義中用信號(hào)的四階非線性變換來代替信號(hào)本身，提出了廣義線性正則變換，并用其來估計(jì)二次調(diào)頻信號(hào)的三階相位系數(shù)；從均方誤差、輸出信噪比及運(yùn)算量等角度研究了本算法的性能，并從這三個(gè)方面與現(xiàn)有的四階非線性變換算法相比較。結(jié)果顯示，與其它算法相比，本算法的均方誤差具有更低的信噪比門限；當(dāng)輸入信噪比滿足一定條件時(shí)，本算法的輸出信噪比要高于其它常見四階非線性變換算法，并且要達(dá)到同樣大小的輸出信噪比，本算法所需的采樣點(diǎn)比其它算法少很多。由于本算法只需一維搜索且線性正則變換具有快速算法，本算法的運(yùn)算量較低，具有較高運(yùn)算效率。 3、提出了基于線性正則變換的模糊函數(shù)的二次調(diào)頻信號(hào)參數(shù)估計(jì)算法。基于線性正則變換的模糊函數(shù)對二次調(diào)頻信號(hào)具有良好的聚焦特性，利用這種聚焦性估計(jì)信號(hào)的二階相位系數(shù)和三階相位系數(shù)，進(jìn)而利用Dechirp技術(shù)和Fourier變換估計(jì)一階相位系數(shù)和幅值。理論分析和仿真結(jié)果表明，由于本算法為二階非線性變換，本算法具有非常低的信噪比門限(-3dB)，相對于具有四階和六階非線性變換的算法而言，低信噪比時(shí)的估計(jì)精度大大提高；通過分析輸入信噪比和輸出信噪比的關(guān)系發(fā)現(xiàn)，在輸入信噪比大于-10dB時(shí)，本算法的輸出信噪比高于基于廣義線性正則變換算法、積分廣義模糊函數(shù)算法和多項(xiàng)式相位變換等算法；當(dāng)輸入信噪比大于7dB時(shí)，要達(dá)到同樣大小的輸出信噪比，本算法所需采樣點(diǎn)數(shù)分別是廣義線性正則變換算法、積分廣義模糊函數(shù)算法和多項(xiàng)式相位算法的采樣點(diǎn)的1/2左右、1/4左右和1/9左右。這說明，在達(dá)到相同大小的輸出信噪比時(shí)，本算法所需的采樣點(diǎn)數(shù)更少。由于本算法能一次估計(jì)出三個(gè)參數(shù)，高階相位系數(shù)對低階相位系數(shù)誤差傳遞小，使得低階系數(shù)的估計(jì)值更為準(zhǔn)確。
[Abstract]:The two frequency modulation signal is a non-stationary signal which exists widely in the field of nature and engineering technology. The time frequency analysis and parameter estimation of the two frequency modulation signal in the noise background are the common problems which it needs to be solved in the practical application. Therefore, it is important to study the detection and parameter estimation of the two frequency modulation signals. Theoretical significance and practical application value.
The traditional two frequency modulation signal parameter estimation algorithm mainly uses the higher order nonlinear transformation to reduce the order, and then uses the existing or constructs the new time-frequency distribution estimation parameters. However, the high order nonlinear transformation of this kind of algorithm will bring high signal to noise ratio threshold and lower output signal to noise ratio, or a large amount of operation. As Fourier transform, the generalized form of fractional order Fourier transform has three free parameters, so it is more flexible and has a fast algorithm, so the computation of the transformation is low. The basic theory of the linear regular transformation and the two frequency modulation parameter estimation algorithm for high performance are discussed. In the light of the advantages and characteristics of signal processing, a new time-frequency distribution based on linear regular transformation is constructed, their related theories are studied, and the application of relevant theoretical results to the estimation of the parameters of the two frequency modulation signal is discussed. The main contributions and innovative results are as follows:
1, in order to study the parameter estimation of two frequency modulation signals, the basic theory of linear regular transformation is first studied. First, a fuzzy function based on linear regular transformation is proposed, and the characteristic properties of the linear regular transform are deeply analyzed and studied; and the fuzzy function and other time based on linear regular transformation are further investigated. The relationship between frequency analysis tools shows that some commonly used time frequency distributions can be expressed by fuzzy functions based on linear regular transformation, and a fuzzy function based on linear regular transformation of common signals is given. The convolution, product property and correlation properties of the fuzzy functions after the linear regular transformation of signals are studied. In this paper, the new time frequency distribution of Wigner-Ville distribution based on linear regular transformation is proposed, and some new important properties are derived. The relationship between the time frequency analysis method and the other time-frequency analysis methods is studied. The Wigner-Ville distribution based on the linear regular transformation of the common signals is analyzed. Finally, the two dimensional linear regular transformation is given. On the basis of some of its common properties, the convolution and product theory of two-dimensional linear regular domain is proposed, and the numerical calculation of the two-dimensional linear regular transformation is verified by an example. The computation of the two-dimensional linear regular transformation is analyzed. The basic theory of the above linear regular transformation is established. On the one hand, it enriches the linear regular transformation further. The theoretical system, on the other hand, has laid a theoretical foundation for studying the parameter estimation algorithm of the two frequency modulation signal.
2, a parameter estimation algorithm for two frequency modulation signals based on generalized linear regular transformation is proposed. In the definition of linear regular transformation, the four order nonlinear transformation of signal is used to replace the signal itself. A generalized linear regular transformation is proposed, which is used to estimate the three phase coefficient of the two frequency modulation signal, and the signal to noise ratio is output from the mean square error and the signal to noise ratio. The performance of this algorithm is studied and compared with the existing four order nonlinear transformation algorithms. The results show that the mean square error of this algorithm has a lower SNR threshold compared with other algorithms. When the input signal to noise ratio satisfies certain conditions, the output signal to noise ratio of this algorithm is higher than that of the other four other four common algorithms. In order to achieve the same size of the output signal to noise ratio of the same size, the algorithm needs less sampling points than other algorithms. Because this algorithm only needs one dimension search and the linear regular transformation has a fast algorithm, the algorithm has low computation and high operation efficiency.
3, a parameter estimation algorithm for the two frequency modulation signal of fuzzy function based on linear regular transformation is proposed. The fuzzy function based on linear regular transform has good focusing characteristic on the two frequency modulation signal. The two order phase coefficient and the three order phase number of the signal are estimated by this focus, and then the Dechirp technology and the Fourier transform are used to estimate the signal. The theoretical analysis and simulation results show that this algorithm has a very low signal to noise ratio threshold (-3dB) because this algorithm is a two order nonlinear transformation. Compared with the four order and six order nonlinear transformation algorithms, the estimated precision of the low signal to noise ratio is greatly improved, and the input signal to noise ratio and the output signal are analyzed. When the input signal-to-noise ratio is greater than -10dB, the output signal-to-noise ratio of this algorithm is higher than that based on the generalized linear regular transform algorithm, the integral generalized fuzzy function algorithm and the polynomial phase transformation algorithm. When the input signal to noise ratio is greater than 7dB, the output signal to noise ratio of the same size should be reached, the number of sampling points required in this algorithm is respectively The sampling points of the generalized linear regular transformation algorithm, the integral generalized fuzzy function algorithm and the polynomial phase algorithm are about 1/2, about 1/4 and 1/9. This shows that the number of sampling points in this algorithm is less when the output signal to noise ratio of the same size is reached. Because this algorithm can estimate three parameters at a time, the high order phase coefficient is to the lower order phase. The transmission error of bit coefficient is small, which makes the estimation value of low order coefficient more accurate.
【學(xué)位授予單位】：北京理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.23

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