Final answer:
The maximum data rate for a telecommunications channel using a copper cable with a 4kHz bandwidth, binary signaling, a raised-cosine pulse, and a 0.5 roll-off factor is 6kbps.
Step-by-step explanation:
The student's question is about calculating the data rate for a telecommunications channel using a copper cable with a 4kHz bandwidth. The data rate can be determined by considering the Nyquist rate which multiplies the bandwidth by the number of signal levels (here, 2 levels, since binary signaling is used). With the raised-cosine filter and a roll-off factor of 0.5, the bandwidth is effectively increased. The raised-cosine filter allows for a higher symbol rate for a given bandwidth without increasing the bit error rate. The roll-off factor indicates how much additional bandwidth is used beyond the Nyquist minimum to shape the signal spectrum and avoid interference. The data rate in bits per second (bps) can be calculated using the formula: Maximum Data Rate = Bandwidth x (1 + Roll-off factor) x log2(2). For binary signaling (2 levels), the log2(2) is 1, and with a roll-off factor of 0.5, the formula simplifies to:
Maximum Data Rate = Bandwidth x 1.5
Therefore, the maximum data rate is:
Maximum Data Rate = 4 kHz x 1.5 = 6kbps