EXAM # 1, EE5352, Spring 2011
1. Let y(n) be the output of linear system with impulse response h(n), where the
input w(n) is a stationary independent noise process applied starting at time zero. In
other words, y(n) = h(n)*w(n) and w(n) = x(n)u(n), where
EXAM # 1, EE5352, Spring 2012
1. Let y(n)=u(a-x(n) where the x(n)'s are zero-mean, independent, and stationary,
and where a is positive. The pdf of x(n) is fx(x).
(a) Find an expression for E[y(n)].
(b) Find E[y(n)y(n+m)].
2. Let x(n) = n + e(n) where e(n
EXAM # 2, EE5352, Spring 2011
1. Let z(n) and d(n) represent stationary, zero-mean random processes.
(a) Give an expression for the Wiener filter error function I, in terms of the
correlations rzz(m) and rzd(m).
(b) Give the normal equations for the filte
EXAM # 2, EE5352, Spring 2012
1. It has been said that the reflection coefficient sequence cfw_Cm can be used to
reconstruct the error sequences cfw_amn in the Levin-Durbin recursion.
(a) In terms of cfw_Cm, show the calculations of a11, a21, a22, a31, a
EXAM # 3, EE5352, Spring 2011
1. Let zi(n) = s(n)+ni(n) where ni(n) is WGN and 1 i Nch. var(ni(n) = v(i), so the
noise variance is different for each channel. The s(n)'s are unknown and 0 n N-1.
(a) Find the LLF for s(m).
(b) Find the MLE of s(m). Is the
EXAM # 3, EE5352, Spring 2012
1. Let zi(n)=a(i)s(n)+ni(n) where ni(n) is white and 1 i Nch
The a(i)'s and s(n)'s are unknown.
(a) Find the log likelihood function ln(f(za,s).
(b) Setting the partial derivatives of the function to zero, find the MLE's for