文档介绍：1Chapter 6Random Processes and Spectral Analysis2Introduction(chapter objectives)?Power spectral density?Matched filters Recall former Chapter that random signals are used to convey information. Noise is also described in terms of statistics. Thus, knowledge of random signals and noise is fundamental to an understanding of communication systems. 3Introduction?Signals with random parameter are random singals ;?All noise that can not be predictable are called random noise or noise ;?Random signals and noise are called random process ;?Random process (stochastic process) is an indexed set of function of some parameter( usually time) that has certain statistical properties. ?A random process may be described by an indexed set of random variables.?A random variable maps events into constants, whereas a random process maps events into functions of the parameter ?Random process can be classified as strictly stationaryor wide-sense stationary;?Definition: A random process x(t) is said to be stationary to the order N if , for any t1,t2,…,tN, :3)-(6))+(),...,+(),+((=))(),...,(),((0020121ttxttxttxftxtxtxfNxNx?Where t0si any arbitrary real constant. Furthermore, the process is said to be strictly stationary if it is stationary to the order N→infinite?Definition: A random process is said to be wide-sense stationary if 15b)-(6)τ(=),(215a)-(6andconstant =)(121xxRttRtx?Where τ=t2-?Definition: A random process is said to beergodic if all time averages of any sample function are equal to the corresponding ensemble averages(expectations)?Note: if a process is ergodic, all time and ensemble averages are interchangeable. Because time average cannot be a function of time, the ergodic process must be stationary, otherwise the ensemble averages would be a function of time. But not all stationary processes are )-(6+σ=>)(<=6c)-(6=)(][=])([6b)-(6])([1lim=)]([6a)-(6][][222∞∞-T/2T/2-∫∫xxrmsxxT→→xdcmtxXmdxxfxtxdttxTtx =mx(t)=x(t)=x6Introduction?De