Texts: Preparation question: Consider the digital signal processing system for noise cancellation using an adaptive filter with two coefficients shown in Figure Q3. The weight update equation is given by w_n = w_n-1 + 2e_nx_n - if i = 0,1.
Assume that w_0 = 0, w_1 = 0, x_1 = 0, and the convergence factor = 0.05. Apply adaptive filtering to obtain outputs y(n) and e(n) for n = 0, 1, 2, as well as filter weights w_0(n) and w_1(n) for n = 0, 1, given inputs d_n and x_n as shown in Table Q3. Copy the table in your answer sheet. Show your calculations.
Signal and noise d_n = s_n + n_n
Output e(n)
Noise (u) x
Adaptive filter
y_n = w_0(n-1)x_n + w_1(n-1)x_n-1
(u) A
Figure Q3
Table Q3 Noise Filter signal output (u) x y(n)
Iteration n
Signal corrupted with noise d(n) -1.5 -1 1
Error signal e(n)
Filter weight w_0(n)
Filter weight w_1(n)
0 1 2
-1 1 -1
