The Schur recursion is a mapping from the autocorrelation sequence rx(k) to a set of reflection coefficients.

(a) Write a MATLAB program that implements the Schur recursion. Using the flops command, compare the efficiency of the Schur recursion to the Levinson-Durbin recursion to find the reflection coefficients Γ_j from an autocorrelation sequence r_x(k).

(b) Derive the inverse Schur recursion that produces the autocorrelation sequence r_x(k) from the reflection coefficients Γ_J, and write a MATLAB program to implement this recursion. Compare the efficiency of the inverse Schur recursion to the inverse Levinson Durbin recursion to find the autocorrelation sequence from the reflection coefficients.