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上海交通大学微弱信号检测Detectionofweaksignal2-Fundamental Concepts of Noise
* Fundamental Concepts- Detection of Weak Signals * 2.3.4 cross-power spectral density(互功率谱密度) By definition, the cross-power spectral density of two stationary processes(稳态过程) is the Fourier transform of their cross-correlation function * Fundamental Concepts- Detection of Weak Signals * 2.3.4 Linear System Assume a linear, lumped, time invariant system(时间不变系统) whose transfer function is H(j). input fluctuation x(t), with known mean and spectral density Sf(x). The spectral density of the fluctuation y(t) obtained at the output is Sf(y) The autocorrelation function is the inverse Fourier transform of Sf(y) * Fundamental Concepts- Detection of Weak Signals * 2.4 Summary Average provides an insight with a constant Rms can be interpreted as a DC voltage , generating same heating with the noise. Almost all noise voltages or currents have a PDF with a Gaussian distribution. Wiener-Khintchier theorem ( autocorrelation and the power spectral density are related by a Fourier transform). * Fundamental Concepts- Detection of Weak Signals * 2.5 Class discussion Please write down five concepts in this chapter according to their importance. For the theories learned so far, please give the conditions which theory is preferred. If you wish to construct a new theory to deal noise, what will be your first step? Why? * Fundamental Concepts- Detection of Weak Signals * 2.3.1 One Random Variable Cumulative distribution function(累积分布函数,CDF) is defined as the probability at instant t1 is less than some specified value x1. * Fundamental Concepts- Detection of Weak Signals * 2.3.1 Averages, variance, standard deviation The first formula is the N-th order average (n-th order moment矩) The most often encountered averages are m1 and m2. The second formula is called variance(方差). The third derivative is called standard deviation(标准偏差). * Fundamental Concepts- Detection of Weak Signals * 2.3.1 Physical Meaning for ergodic processes The mean value: DC component The square of the first order
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