Write a computer simulation of the PLL estimation problem. Do this by generating two independent Gaussian random

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Write a computer simulation of the PLL estimation problem. Do this by generating two independent Gaussian random variables to form Zand Zgiven by (11.196). Thus, for a given (11.201). Call the first value Î¸0. Estimate the next value of θ, call it θ1, from the algorithm.

Z20 0, = 0, + e tan¬ %3D '1,0

where Z1,0 and Z2,0 are the first values of Z1 and Z2 generated and É› is a parameter to be varied (choose the first value to be 0.01). Generate two new values of Z1 and Z2 (call them Z1,1 and Z2,1) and form the next estimate according to 

Z21 02 = 0, + e tan¬! '2,1

Continue in this fashion, generating several values of θ1. Plot the θis versus i, the sequence index, to determine if they seem to converge toward zero phase. Increase the value of ɛ by a factor of 10 and repeat. Can you relate the parameter ɛ to a phase-lock loop parameter (see Chapter 4)? This is an example of Monte Carlo simulation.

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