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HW 8 Questions

# HW 8 Questions - estimate s(k(filtering(a Find the Wiener...

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ECE 408 HOMEWORK #8 1. Suppose that a signal x(k) = s(k) + w(k), where s(k) is an AR(1) process that satisfies the difference equation s(k) = 0.8 s(k 1) + v(k), where v(k) is a white noise sequence with variance σ v 2 = 0.36 and w(k) is a white noise process with variance σ w 2 = 1.2, is applied to an FIR Wiener filter with length M = 3 to estimate s(k) (filtering). (a) Find the Wiener filter coefficients h(0), h(1), and h(2). (b) Find the minimum mean-square error when the coefficients obtained in (a) is used. 2. Suppose that a signal x(k) = s(k) + w(k), where s(k) is an AR(1) process that satisfies the difference equation s(k) = 0.8 s(k 1) + v(k), where v(k) is a white noise sequence with variance σ v 2 = 0.36 and w(k) is a white noise process with variance σ w 2 = 1.2, is applied to an FIR Wiener filter with length M = 4 to
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Unformatted text preview: estimate s(k) (filtering). (a) Find the Wiener filter coefficients h(0), h(1), h(2), and h(3). (b) Find the minimum mean-square error when the coefficients obtained in (a) is used. 3. Suppose that the coefficients of the 3-tap adaptive FIR filter are set to zero initially, that is, w (0) = 0, w 1 (0) = 0, w 2 (0) = 0. The subscript represents coefficient number and the number inside the parenthesis represents time. The input signal to the adaptive FIR filter is given by x(0) = 1.1, x(1) = 0.3, x(2) = -0.8, x(3) = -0.2, x(4) = 1.2, x(5) = 0.25 and the desired signal is given by d(0) = 1, d(1) = 0, d(2) = -1, d(3) = 0, d(4) = 1, d(5) = 0 Find the output y(k), e(k) for k = 0, 1, 2, 3, 4, 5. Also find the coefficients w (k), w 1 (k), and w 2 (k) for k = 1, 2, 3, 4, 5. Assume that µ = 0.1. 1...
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