E&CE 358: Tutorial-4 Instructor: Prof. Xuemin (Sherman) Shen TA: Miao Wang 1

Review of Random Processes Mean of the random process X(t): is the mean of random variable X(t) at time instant t. Correlation function of X(t): is a function of two variables t1 = t and t2 = t + τ, which is a measure of the degree to which two time samples of the same random process are related

Review of WSS Processes Wide-Sense Stationary (WSS) Process: A random process X(t) is Wide-Sense Stationary (WSS) if Here, we can see a random process X(t) is WSS if its mean and correlation, do not vary with a shift in the time origin.

Review of WSS Processes Properties of Correlation Function :

Review of WSS Processes Power Spectral Density (PSD): For a given WSS process X(t), the psd of X(t) is the Fourier transform of its correlation,i.e. Properties of PSD:

Review of WSS Processes Properties of the output in transmission system