Consider Equation (4.108), which defines the impulse response of a minimum mean- square error receiver.

(a) Justify the validity of Equation (4.109) that is the Fourier-transformed version of Equation (4.108).

(b) The power spectral density S_q (ƒ) in Equation (4.109) is the Fourier transform of the autocorrelation R_q (τ₁, τ₂) of the time function q (t). The R_q (τ₁, τ₂) is defined by Equation (4.98). Starting with Equation (4.98), derive the formula of Equation (4.111).

1, 10, n=0 1, 2, . . . , tN ken-k - Received signal Tapped-delayOutput Transmitted signal Linear channel ecualizer