1. Ideal Channel (Noiseless Channel): According to Nyquist Theorem, the maximum numbers of bits (I.e., Theoretical Limit) that can be transmitted over an ideal communication link cannot exceed to

C: maximum number of bits can be transmitted per sec (bps)

B: Channel Bandwidth (Hz)

M: # of discreet levels in a signal (depends on which modulation scheme we are using)

2B: Baud Rate or Modulation Rate (# of samples generated per seconds)

log₂(M) will provide how many bits transmitted per sample

2. Practical Channel (Noisy Channel) Shannon Theorem:

For a practical channel, we must consider SNR of the channel when measuring the channel capacity. Therefore, the above formula can be modified as:

C: maximum number of bits can be transmitted per sec (bps)

B: Channel Bandwidth (Hz)

SNR (absolute): ratio of signal power to noise power

Note:

-----------------------------------use above methods

Sample Question 1: Consider an extremely noisy channel in which the value of the signal-to-noise ratio is almost zero. In other words, the noise is so strong that the signal is faint. For this channel, compute the capacity C when the bandwidth is 1MHz. What can be concluded based on the final value of C

Sample Question 2: Calculate the theoretical highest bit rate (i.e., C) of a regular telephone line. A telephone line normally has a bandwidth of 3000Hz. The signal-to-noise ratio for such a link is usually 3162 (absolute value).

Sample Question 3: The signal-to-noise ratio is often given in decibels. Assume that SNR_dB = 36dB and the channel bandwidth is 2 MHz. Determine the theoretical channel capacity in bps.

B. What would be the minimum permissible SNR (in dB) for the data rate calculated in part (a)?

Question 1: A telephone line has a bandwidth of 3.2 kHz and a SNR of 35 dB. A signal is transmitted down this line using a 4-level code. What is the maximum theoretical data rate for both noisy and noiseless channel? Noiseless Channel Noisy Channel Question 2: A broadcast TV channel has a bandwidth of 6 MHz. a) Calculate the maximum data rate that could be carried in a TV channel using 16-level code. Ignore noise Page 2 of 4 WS 42 - Edited 125% T View Zoom Add Page Insert Table Chart Text Shape Media Comment Colla! Question 3: Suppose that the bandwidth is 1MHz and SNR = 24dB. Find a) Maximum data rate that can be transmitted over a communication channel b) How many signaling levels (i.e., M) are required to transmit the data we found in part (a). Part (a) Part (b) Question 4: What is the (i) data rate (bps) (ii) and # of signaling levels for a tele-printer channel with a 300 Hz bandwidth and SNR of 3 dB (i) Data Rate (ii) # of signaling levels Page 3 of 4 5 o A IJ o VWS 4 2 - Edited 125% BE T E 6 View Zoom Add Page Insert Table Chart Text Shape Media Comment Colla Question 4: What is the (i) data rate (bps) (ii) and # of signaling levels for a tele-printer channel with a 300 Hz bandwidth and SNR of 3 dB (i) Data Rate (ii) # of signaling levels Page 3 of 4 Question 5: Determine the bandwidth for a communication channel that has an SNR of 35 dB and capable of transmitting the data rate at 37.2 Kbps. 1 o IJ "DOCK WS 42 - Edited 125% T 6 View Zoom Add Page Insert Table Chart Text Shape Media Comment Colla Question 5: Determine the bandwidth for a communication channel that has an SNR of 35 dB and capable of transmitting the data rate at 37.2 Kbps. Question 6: Find the Baud Rate for a noisy channel that can transmit only 2.3 Kbps (unrealistic data rate) with SNR of -10dB. Page 4 of 4 Question 1: A telephone line has a bandwidth of 3.2 kHz and a SNR of 35 dB. A signal is transmitted down this line using a 4-level code. What is the maximum theoretical data rate for both noisy and noiseless channel? Noiseless Channel Noisy Channel Question 2: A broadcast TV channel has a bandwidth of 6 MHz. a) Calculate the maximum data rate that could be carried in a TV channel using 16-level code. Ignore noise Page 2 of 4 WS 42 - Edited 125% T View Zoom Add Page Insert Table Chart Text Shape Media Comment Colla! Question 3: Suppose that the bandwidth is 1MHz and SNR = 24dB. Find a) Maximum data rate that can be transmitted over a communication channel b) How many signaling levels (i.e., M) are required to transmit the data we found in part (a). Part (a) Part (b) Question 4: What is the (i) data rate (bps) (ii) and # of signaling levels for a tele-printer channel with a 300 Hz bandwidth and SNR of 3 dB (i) Data Rate (ii) # of signaling levels Page 3 of 4 5 o A IJ o VWS 4 2 - Edited 125% BE T E 6 View Zoom Add Page Insert Table Chart Text Shape Media Comment Colla Question 4: What is the (i) data rate (bps) (ii) and # of signaling levels for a tele-printer channel with a 300 Hz bandwidth and SNR of 3 dB (i) Data Rate (ii) # of signaling levels Page 3 of 4 Question 5: Determine the bandwidth for a communication channel that has an SNR of 35 dB and capable of transmitting the data rate at 37.2 Kbps. 1 o IJ "DOCK WS 42 - Edited 125% T 6 View Zoom Add Page Insert Table Chart Text Shape Media Comment Colla Question 5: Determine the bandwidth for a communication channel that has an SNR of 35 dB and capable of transmitting the data rate at 37.2 Kbps. Question 6: Find the Baud Rate for a noisy channel that can transmit only 2.3 Kbps (unrealistic data rate) with SNR of -10dB. Page 4 of 4