Digital signal processing question:

3. Consider the random signal with first order probability density function (3-1) 0, else For this random variable, consider an optimal 2-level quantizer defined by the following memoryless input-output mapping Q0) (3-2) X3xs2 We showed in class that the optimal quantizer satisfies the following set of coupled fx(r)dx ?. (3-3) fr (x)dr fr (x)dr For the specific density function given by Eq. (3-1), evaluate the integrals in Eq. (3-3) to obtain closed form expressions for the functions ?(h) , ?(4) and ?(y0.y?) a. We also discussed in class a simple iterative procedure for determining a set of values for X o.and y that simultaneously satisfy Eq. 3-3). b. Write a Matlab program to implement this procedure. Execute the program, and run it until you obtain satisfactory convergence. Turn in your M-file and plots of x1 , y0 , and y, as a function of the iteration number 3. Consider the random signal with first order probability density function (3-1) 0, else For this random variable, consider an optimal 2-level quantizer defined by the following memoryless input-output mapping Q0) (3-2) X3xs2 We showed in class that the optimal quantizer satisfies the following set of coupled fx(r)dx ?. (3-3) fr (x)dr fr (x)dr For the specific density function given by Eq. (3-1), evaluate the integrals in Eq. (3-3) to obtain closed form expressions for the functions ?(h) , ?(4) and ?(y0.y?) a. We also discussed in class a simple iterative procedure for determining a set of values for X o.and y that simultaneously satisfy Eq. 3-3). b. Write a Matlab program to implement this procedure. Execute the program, and run it until you obtain satisfactory convergence. Turn in your M-file and plots of x1 , y0 , and y, as a function of the iteration number