Question 10 In this question we explore the application of MAP and LMS estimation in a communication channel. Suppose we want to send a signal X, but this is corrupted by additive noise N such that the signal at the receiver is Y, where Y = X+ N. We assume the noise is Gaussian with zero mean and a known variance, i.e., N ~ N(0, o²). We further assume that X is a continuous random variable with half of the probability clustered at +1 and half of the probability clustered at -1. (We say this, instead of calling X a discrete random variable, is so that the estimate does not necessarily have to be ±1. We can formalize it in more rigorous mathematics using a delta function, but that is beyond the scope of this class.) 1. Find the MAP estimate of X. 2. Find the LMS estimate of X.
Question 10 In this question we explore the application of MAP and LMS estimation in a communication channel. Suppose we want to send a signal X, but this is corrupted by additive noise N such that the signal at the receiver is Y, where Y = X+ N. We assume the noise is Gaussian with zero mean and a known variance, i.e., N ~ N(0, o²). We further assume that X is a continuous random variable with half of the probability clustered at +1 and half of the probability clustered at -1. (We say this, instead of calling X a discrete random variable, is so that the estimate does not necessarily have to be ±1. We can formalize it in more rigorous mathematics using a delta function, but that is beyond the scope of this class.) 1. Find the MAP estimate of X. 2. Find the LMS estimate of X.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 29E
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