本文選題：隨機共振　切入點：弱信號　出處：《青島大學》2014年博士論文　論文類型：學位論文

【摘要】：隨機共振是研究一些非線性系統(tǒng)中噪聲的積極建設(shè)性作用的一類物理現(xiàn)象。本文在深入研究隨機共振和循環(huán)平穩(wěn)理論的基礎(chǔ)上,在弱周期信號條件下,利用信噪比和費舍爾信息量進一步研究隨機共振現(xiàn)象,并且找到了二者之間的關(guān)聯(lián)。費舍爾信息量能夠描述幾個重要非線性處理過程中的性能；一個局部最優(yōu)處理器能夠獲得最大輸出輸入信噪比,最大輸出輸入信噪比增益是由標準噪聲分布的費舍爾信息量給定的,并且最大信噪比增益是靜態(tài)非線性元素組成的陣列的信噪比增益的上限。在本論文中,又進一步的對靜態(tài)和動態(tài)非線性系統(tǒng)的隨機共振現(xiàn)象進行了對比。論文的主要研究成果如下： 1.最初費舍爾信息量是作為參數(shù)估計的性能指標。我們將它擴展并且表明費舍爾信息量能夠描述幾個重要非線性處理過程中的性能。對于加性白噪聲中的弱信號,費舍爾信息量能決定如下四個方面：(i)周期信號的最大輸出信噪比；(ii)信號檢測的最優(yōu)漸近性能；(iii)信號傳輸?shù)淖顑?yōu)互相關(guān)系數(shù)；(iv)無偏估計值的最小均方差。通過費舍爾信息量不等式,這個統(tǒng)一的結(jié)論用于建立通過噪聲改善隨機共振是否可行的條件。 2.通過噪聲概率密度和噪聲強度能精確地決定一個局部最優(yōu)處理器,并且局部最優(yōu)處理器的輸出輸入信噪比增益是由標準噪聲分布的費舍爾信息量給定的�；谶@個關(guān)聯(lián),我們發(fā)現(xiàn)對于局部最優(yōu)處理器,能夠獲得比一任意大的信噪比增益。對于隨機共振,考慮向已知信號中加入額外噪聲時,我們證明了通過費舍爾信息量不等式,和新噪聲完全匹配的更新的局部最優(yōu)處理器,不能改進輸出信噪比以超過無額外噪聲時所對應(yīng)的初始值。這個結(jié)果印證了一個以前只對高斯噪聲存在的定理。此外,在參數(shù)不可調(diào)處理器的情況下,比如由噪聲概率密度描述的局部最優(yōu)處理器的結(jié)構(gòu)不能完全適應(yīng)噪聲強度時,表明了可以恢復隨機共振的一般條件,通過添加額外聲提高輸出信噪比的可能性來證明。 3.研究了為傳輸在加性白噪聲中的弱周期信號,由任意的靜態(tài)非線性元素組成的非耦合并聯(lián)陣列的輸出輸入信噪比增益。在小信號的限制條件下,推導出信噪比增益的一個漸近表達式。并且證明了對任意給定的非線性系統(tǒng)和噪聲環(huán)境,信噪比增益是關(guān)于陣列大小的單調(diào)遞增的函數(shù)。由局部最優(yōu)非線性系統(tǒng)所對應(yīng)的信噪比增益,是靜態(tài)非線性元素組成的陣列的信噪比增益的上限。在局部最優(yōu)非線性系統(tǒng)中,隨機共振不能發(fā)生,也就是說,在陣列中加入內(nèi)部噪聲不能改善信噪比增益。然而,在一個由次優(yōu)但易實現(xiàn)的閾值非線性系統(tǒng)組成的陣列中,我們證明了隨機共振發(fā)生的可行性,也證明了對于各種內(nèi)部噪聲分布,信噪比增益大于一的可能性。 4.利用輸出信噪比作為測量方法,比較了靜態(tài)和動態(tài)非線性系統(tǒng)的隨機共振現(xiàn)象。對于給定的含噪弱周期信號,通過調(diào)諧內(nèi)部噪聲強度,靜態(tài)和動態(tài)非線性并聯(lián)陣列都能提高輸出信噪比。靜態(tài)非線性系統(tǒng)容易實現(xiàn),而動態(tài)非線性系統(tǒng)有較多參數(shù)需要調(diào)整,存在不能利用內(nèi)部噪聲的有利作用的風險。并且外部噪聲是非高斯類型時,可以觀察到動態(tài)非線性系統(tǒng)是優(yōu)于靜態(tài)非線性系統(tǒng),可以獲得一個更好的輸出信噪比,證明了加入額外白噪聲以提高輸出信噪比的可能性。
[Abstract]:Stochastic resonance is a physical phenomenon of some noise in nonlinear systems, a positive and constructive role. Based on the study of stochastic resonance and cyclostationary theory, the weak periodic signal conditions, the SNR and Fisher information to further study the stochastic resonance phenomenon, and find the correlation between the two. Fisher information to describe the performance of several important nonlinear process; a local optimal processor can obtain maximum output SNR, maximum output SNR gain is the amount of information given by the standard Fisher noise distribution, and the maximum SNR gain is a nonlinear static element array noise than the gain limit. In this paper, compared further on the static and dynamic nonlinear systems with stochastic resonance phenomenon. The main research The results are as follows:
1. of the original Fisher information is as the performance parameter estimation. We expand it and show that Fisher information can describe the performance of several important nonlinear process. For weak signal of additive white noise, Fisher decided the volume of information in four aspects as follows: (I) periodic signal maximum output signal-to-noise ratio; (II) the optimal asymptotic performance of signal detection; (III) optimal signal transmission cross correlation coefficient; (IV) an unbiased estimate of the minimum variance. By Fisher information inequality, the unified conclusion for establishing through noise improved stochastic resonance is feasible conditions.
2. the noise probability density and noise intensity can accurately determine a local optimal processor and local optimal processor output SNR gain is the amount of information given by Fisher standard noise distribution. Based on this association, we found that the local optimal processor, can earn more than a arbitrarily large signal-to-noise ratio gain. For stochastic resonance, consider adding additional noise to the known signals, we show that the amount of information through the Fisher inequality, the local optimal processor and new noise, completely updated, can improve the output SNR with no additional noise exceeds the initial value corresponding. This result confirms a previously only on Gauss noise existence theorem. In addition, the parameter adjustable processor case, such as local optimal processor structure can not be described by the noise probability density of fit In the case of noise intensity, the general condition of restoring the random resonance is shown, and the possibility of increasing the output signal to noise ratio by adding extra sound is proved.
3. studies for the weak periodic signal in additive white noise in transmission, non coupled parallel arrays composed of a nonlinear static element of arbitrary input and output SNR gain. Constraints on the small signal, the signal-to-noise ratio is derived. An asymptotic expression for the gain and the nonlinear system and noise environment for any given, the SNR gain is a function of the size of the array is monotonically increasing. The signal-to-noise ratio gain corresponding by local optimal nonlinear systems, nonlinear static element array is SNR gain limit. In local optimal nonlinear systems, stochastic resonance can occur, that is to say, adding the internal noise in the array can improve the signal-to-noise ratio gain. However, in an array composed of threshold nonlinear suboptimal but easy to implement in, we demonstrate the feasibility of stochastic resonance, also proved For all kinds of internal noise distribution, the gain of signal to noise ratio is more than one possibility.
4. the output signal-to-noise ratio as a measurement method, compare the stochastic resonance phenomenon of the static and dynamic nonlinear systems. For a given noisy weak periodic signal, by tuning the internal noise intensity, the static and dynamic nonlinear parallel array can improve the output SNR. The static nonlinear system is easy to implement, and dynamic nonlinear system many parameters need to be adjusted, there can not use risk beneficial effects of internal noise and external noise. The non Gauss type, can be observed in the nonlinear dynamic system is superior to static nonlinear system, and can obtain a better output signal-to-noise ratio, it is proved that adding additional white noise probability to improve the output SNR.

【學位授予單位】：青島大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TN911.7

【參考文獻】

相關(guān)期刊論文 前7條

1 祝恒江,吳錫田;隨機共振研究進展[J];大學物理;1997年07期

2 王利亞,蔡文生,印春生,潘忠孝;一種有效提取弱信號的新方法[J];高等學�；瘜W學報;2000年01期

3 趙廷玉;張文字;葉子;余飛鴻;;應(yīng)用費希爾信息量評價函數(shù)的波前編碼系統(tǒng)設(shè)計[J];光學學報;2007年06期

4 黃繼偉;李云飛;朱宏;;刪失數(shù)據(jù)下的Fisher信息量[J];電子科技大學學報;2006年03期

5 王利亞,沈陽,潘忠孝,張懋森;隨機共振應(yīng)用初步研究[J];計算機與應(yīng)用化學;2000年Z1期

6 李華鋒,徐博侯;隨機共振系統(tǒng)輸出的一種新的反演方法　[J];力學學報;2003年02期

7 甘春標;Perc Matjaz;王青云;;Delay-aided stochastic multiresonances on scale-free FitzHugh-Nagumo neuronal networks[J];Chinese Physics B;2010年04期

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