please help with this question Depicts the use of a modifi

please help with this question : )

Depicts the use of a modified 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 operation1, d_k = b_k circled plus 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) From the block diagram, y_k=XOR(a_k, a_k-2)

b) Decoding rule:

If the received signal is negative, then it is decoded as logic 0.

If the received signal is positive, then it is decoded as logic 1