Suppose that a given speech signal {UR ER:k= 1,..., n} is transmitted over a telephone cable with input-output behavior given by, yk = ayk-1 + buk + Uk, where, at each time k, yk R is the output, Uk E R is the input (speech signal value) and Uk represents the white noise[] The parameters a, b are fixed known constants, and the initial condition is yo = 0. 'If Ar+w = b, where w is a white noise vector, then the least squares estimate of a given b is the soltuion to the problem minimize ||Ac ||? Note than if w is a white noise vector, DW (where D is a matrix) is not neccesarily a white noise vector. 2 We can measure the signal yk at the output of the telephone cable, but we cannot directly measure the desired signal uz or the noise signal uk. Derive a formula for the linear least squares estimate of the signal {ux, k = 1,..., n} given the signal {Yk, k = 1,...,n}. Suppose that a given speech signal {UR ER:k= 1,..., n} is transmitted over a telephone cable with input-output behavior given by, yk = ayk-1 + buk + Uk, where, at each time k, yk R is the output, Uk E R is the input (speech signal value) and Uk represents the white noise[] The parameters a, b are fixed known constants, and the initial condition is yo = 0. 'If Ar+w = b, where w is a white noise vector, then the least squares estimate of a given b is the soltuion to the problem minimize ||Ac ||? Note than if w is a white noise vector, DW (where D is a matrix) is not neccesarily a white noise vector. 2 We can measure the signal yk at the output of the telephone cable, but we cannot directly measure the desired signal uz or the noise signal uk. Derive a formula for the linear least squares estimate of the signal {ux, k = 1,..., n} given the signal {Yk, k = 1,...,n}