Consider a linear model with mean value function t and a signal t delayed by an amount j on each sensor, i.e., yjt = t

Consider a linear model with mean value function µt and a signal αt delayed by an amount τj on each sensor, i.e., yjt = µt + αt−τj + vjt .

Show the estimators (7.42) for the mean and the signal are the Fourier transforms of Mˆ (ω) =

Y·(ω) − φ(ω)Bw(ω)

1 − |φ(ω)|2 and Aˆ(ω) =

Bw(ω) − φ(ω)Y·(ω)

1 − |φ(ω)|2

, where

φ(ω) =

1 N

Õ

N j=1 e

2πiωτj and Bw(ω) is defined in (7.64).