随机过程的概念与定义.ppt

第2章 随机过程的基本概念 2.1 随机过程的基本概念和定义 2.2 随机过程的统计描述 2.3 平稳随机过程 2.4 随机过程的联合分布和互相关函数 2.5 随机过程的功率谱 2.6 典型随机过程 2.7 基于Matlab的统计分析 2.8 信号处理实例 本章学习要点： （1）要注意对基本概念的理解 （2）要注意运用随机变量的理论 （3）掌握统计特性的计算方法 （4）掌握平稳随机过程相关函数与功率谱的特性 （5）注意运用MATLAB建立随机过程直观的印象 本章是本课程的基础和核心 第二章研讨题： 1、二元传输信号(Binary Transmission Signal) 用无数次掷硬币的随机试验来定义一个随机过程：每个时间周期T的取值是1或-1，依赖于投掷硬币是正面还是反面。每次投掷是独立的。 定义一个新的随机过程， 其中t0在（0,T）上均匀分布。 （1）用MATLAB画出随机过程Y(t)的样本函数（3条）； （2）求Y(t)的均值与方差； （3）求Y(t)的一维概率密度； （4）求Y(t)的自相关函数； （5）求Y(t)的功率谱 2. PSDs of Digital modulation Formats Suppose we have a sequence of data symbols (Bk) that we wish to convey across some communication medium. We can use the data symbols to determine the amplitude of a sequence of pulses (This is called pulse amplitude modulation (PAM). If the pulse amplitudes are represented by the sequence of random variables {. . . ,A−2,A−1,A0,A1,A2, . . .} and the basic pulse shape is given by the waveform p(t), Where T is symbol interval (that is, one pulse is launched every T seconds) and  is a random delay, which we take to be uniformly distributed over [0, T) and independent of the pulse amplitudes. (1) Determine the mean, ACF and PSD of S(t); (2) Suppose the pulse amplitudes are an IID sequence of random variables that are equally likely to be +1 or −1. Determine and Plot the a realization of S(t) and PSD of S(t) (3) Suppose In the previous example, we formed the pulse amplitudes according to Ak = Bk. Suppose instead that we formed these amplitudes according to Ak = Bk + Bk−1 Determine and Plot the a realization of S(t) and PSD of S(t) (4) Discuss the PSDs of two cases Reference book: 《Probability and Random Processes with Applications to Signal Processing and Communication》 397-403 4. A binary phase shift keying signal is defined according to for all n, and B[n] is a discrete time, Bernoulli random process that has values of +1 or −1. (a) Determine the autocorrelation function for the X(t). Is the process WSS? (b) Determine the power spectral density