In this problem you are to estimate a parameter of a

1.5

second sample of an ergodic noise process b[n] based upon information from the autocorrelation function φ_bb [k] and/or the power spectral density S_bb(Ω). The process is similar to the one that produced b[n] in Laboratory Exercise 6.1c but now the random variable has value +1 with probability p and value 0 with probability 1–p. Let us call this “unfair” binary noise. (Why the term “unfair”?)

Each time you perform this exercise by pressing the “retry” button below () another sample of the process will be generated but with a new, probably different value for p. The value of p will be chosen randomly from the set {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9}. You will notice that no estimate of the probability density function is presented. You can use the “Zoom” slider to examine the details of the various graphs.

1. Based upon the data shown in the bottom row, is it reasonable to conclude that b[n], an “unfair” binary process, is a sample of a white noise process? Explain your reasoning.


2. Based upon N and the autocorrelation φ_bb [k=0], estimate the value of p that was used to generate this sample. Call this estimate p₁


3. Based upon N and the power spectral density S_bb(Ω=0) as well as φ_bb [k=0], estimate the value of p that was used to generate this sample. Call this estimate p₂


4. It should be clear what the true value of p is for each experiment, each time another value for p is randomly chosen from the set given above. By what percentage do p₁ and p₂ differ from p? From each other?