please help with this question Depicts the use duobinary co

please help with this question :^)

Depicts the use duobinary conversion filter for the transmission of binary data bit stream through a band-limited channel. The following precoding and bit mapping operations are implemented prior to the filtering operation: d_k = b_k d_k-2 = {1, b_k notequalto d_k-2 0, b_k = d_k-2 a_k = {+1, b_k = 1 -1, b_k = 0 Determine the relationship between the output sequence {y_k} and the data pulse sequence {a_k}. Determine the decoding rule based on the sequence {y_k} sampled at the output of the modified duobinary conversion filter. Consider the transmission of the data bit stream {1 0 1 0 1 1 1 0 0 0 1 1 0 1 0}. Assume the two initial precorded bits (d_2, d_1) = (0, 0). Tabulate the data bit stream {b_k}, the precorded bit stream {d_k}, the transmitted pulse sequence {a_k}, the sampled filter output sequence {y_k}, and the decoded sequence {b_k} using the same table format found in a pertinent example in Lecture Notes #7.

Solution

a) y_k=XOR(a_k,a_k-2)

b) y_k is logic 0 when the received signal is negative

  y_k is logic 1 when the received signal ispositive