Topic 7: Random Processes
ES150 { Harvard SEAS 4. ... † Their joint behavior is completely specifled by the joint distributions for all combinations of their time samples. ... Xn = §1 with probability 1 2 for n even Xn = ¡1=3 and 3 with probabilities 9 10 and 1 10 for n odd † Properties of a WSS process:
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The autocorrelation function and the rate of change
www.ece.tufts.eduWhite noise † Band-limited white noise: A zero-mean WSS process N(t) which has the psd as a constant N0 2 within ¡W • f • W and zero elsewhere. { Similar to white light containing all frequencies in equal amounts.
Lecture 1: Entropy and mutual information
www.ece.tufts.edu4.1 Non-negativity of mutual information In this section we will show that I(X;Y) ≥ 0, (27) and this is true for both the discrete and continuous cases. Before we get to the proof, we have to introduce some preliminary concepts like Jensen’s in-equality and the relative entropy.
Topic 6: Convergence and Limit Theorems
www.ece.tufts.eduTopic 6: Convergence and Limit Theorems ... – This is the Central Limit Theorem (CLT) and is widely used in EE. ES150 – Harvard SEAS 7 • Examples: 1. Suppose that cell-phone call durations are iid RVs with μ = 8 and σ = 2 (minutes). – Estimate the probability of 100 calls taking over 840 minutes.
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