ake a look at Figure 3.15 and you'll get a feel for what the inverse system does; (2) in words, if I take a signal x(t), and pass it through the LTI system with impulse response h(t), and then pass it through the inverse system, I get back my original X (t); (3) mathematically, the inverse system is characterized as the system with impulse response h-1(t) (H -1(f)) such that: (3.17) H-((f).H(f)=1 (3.18) 3.4 Onward We've come to the end of our rather brief review. I'll see you as we move ahead into the heart of telecommunications, starting with Chapter 4. A Review of Some Important Math, Stats, and Systems Problems 1. Consider a random variable with probability distribution function (Q3.1) (a) Evaluate the mean. (b) Figure out the variance. 2. Consider a random process where Px(1),x(12) (Q3.2) Mx(1))=0 (Q3.3) Determine the value of the autocovariance. 3. Show that (Q3.4) 4. Determine the Fourier transform of the time signal (1)=16 -T/2SIST/2 (Q3.5) Chapter Source Coding and Decoding: Making it Digital chapter talks about how to turn an analog signal into a digital one, a process called source coding. We took a brief look at it at the end of Chapter 1, when Monica's analog speech signal was turned into a digital signal. We'll now talk at some length about source coding. Before going on, just a brief reminder about why we want to turn analog signals to digital. So many naturally occurring sources of information are analog (human speech, for example), and we want to make them digital signals SO we can use a digital commu- nication system. 4.1 Sampling The key first step in turning any analog signal to a digital one is called sampling. Sampling is the changing of an analog signal to samples (or pieces) of itself. 4.1.1 Ideal Sampling There are three methods of sampling that we'll look at together, the first of which is called ideal sampling, or impulse train sampling. As the name suggests, it is a sam- pling that is impossible to physically carry out. So, you ask, why are you telling me about something that can never 