本文選題：隨機(jī)共振　切入點(diǎn)：弱信號(hào)　出處：《青島大學(xué)》2014年博士論文　論文類型：學(xué)位論文

【摘要】：隨機(jī)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(jī)共振和循環(huán)平穩(wěn)理論的基礎(chǔ)上,在弱周期信號(hào)條件下,利用信噪比和費(fèi)舍爾信息量進(jìn)一步研究隨機(jī)共振現(xiàn)象,并且找到了二者之間的關(guān)聯(lián)。費(fèi)舍爾信息量能夠描述幾個(gè)重要非線性處理過(guò)程中的性能；一個(gè)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(biāo)準(zhǔn)噪聲分布的費(fèi)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(jìn)一步的對(duì)靜態(tài)和動(dòng)態(tài)非線性系統(tǒng)的隨機(jī)共振現(xiàn)象進(jìn)行了對(duì)比。論文的主要研究成果如下： 1.最初費(fèi)舍爾信息量是作為參數(shù)估計(jì)的性能指標(biāo)。我們將它擴(kuò)展并且表明費(fèi)舍爾信息量能夠描述幾個(gè)重要非線性處理過(guò)程中的性能。對(duì)于加性白噪聲中的弱信號(hào),費(fèi)舍爾信息量能決定如下四個(gè)方面：(i)周期信號(hào)的最大輸出信噪比；(ii)信號(hào)檢測(cè)的最優(yōu)漸近性能；(iii)信號(hào)傳輸?shù)淖顑?yōu)互相關(guān)系數(shù)；(iv)無(wú)偏估計(jì)值的最小均方差。通過(guò)費(fèi)舍爾信息量不等式,這個(gè)統(tǒng)一的結(jié)論用于建立通過(guò)噪聲改善隨機(jī)共振是否可行的條件。 2.通過(guò)噪聲概率密度和噪聲強(qiáng)度能精確地決定一個(gè)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(biāo)準(zhǔn)噪聲分布的費(fèi)舍爾信息量給定的。基于這個(gè)關(guān)聯(lián),我們發(fā)現(xiàn)對(duì)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(duì)于隨機(jī)共振,考慮向已知信號(hào)中加入額外噪聲時(shí),我們證明了通過(guò)費(fèi)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(jìn)輸出信噪比以超過(guò)無(wú)額外噪聲時(shí)所對(duì)應(yīng)的初始值。這個(gè)結(jié)果印證了一個(gè)以前只對(duì)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(qiáng)度時(shí),表明了可以恢復(fù)隨機(jī)共振的一般條件,通過(guò)添加額外聲提高輸出信噪比的可能性來(lái)證明。 3.研究了為傳輸在加性白噪聲中的弱周期信號(hào),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(hào)的限制條件下,推導(dǎo)出信噪比增益的一個(gè)漸近表達(dá)式。并且證明了對(duì)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(duì)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(jī)共振不能發(fā)生,也就是說(shuō),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(gè)由次優(yōu)但易實(shí)現(xiàn)的閾值非線性系統(tǒng)組成的陣列中,我們證明了隨機(jī)共振發(fā)生的可行性,也證明了對(duì)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(cè)量方法,比較了靜態(tài)和動(dòng)態(tài)非線性系統(tǒng)的隨機(jī)共振現(xiàn)象。對(duì)于給定的含噪弱周期信號(hào),通過(guò)調(diào)諧內(nèi)部噪聲強(qiáng)度,靜態(tài)和動(dòng)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(shí)現(xiàn),而動(dòng)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(fēng)險(xiǎn)。并且外部噪聲是非高斯類型時(shí),可以觀察到動(dòng)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(gè)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(xué)位授予單位】：青島大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.7

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