Optimum coefficients of the adaptive transversal

Question

Response to the following problem:

Consider the adaptive FIR filter shown in Figure . The system C(z) is characterized by the system function

C(z) = 1/1-0.9z^-1

Determine the optimum coefficients of the adaptive transversal (FIR) filter B(z) = b₀ + b₁z^-1 that minimize the mean square error. The additive noise is white with variance σ²w = 0.1.