Problems on Data and Signals 1. Consider a noiseless channel with a bandwidth of 3000 Hz transmitting a signal with four signal levels. What is the maximum bit rate? 2. We need to send 265 Kbps over a noiseless channel with a bandwidth of 20 kHz. How many signal levels do we need? 3. A telephone line can normally transmit frequencies in the range 300 to 3300 Hz, and the signal-to-noise ratio is typically 3162. Estimate the capacity of this channel in bps. 4. A line has a signal-to-noise ration of 2000 and a bandwidth of 5000 KHz. What is the maximum data rate supported by this line? 5. What are the propagation time and the transmission time for a 2.5 kbyte message if the bandwidth of the network is 1 Gbps? Assume that the distance between the sender and the receiver is 12,000 Km and that light travels at 2.4 × 108 m/s. 6. What is the total delay (latency) for a frame of size 10 million bits that is being sent on a link with 15 routers each having a queuing time of 2 µs and a processing time of 1 µs. The length of the link is 3000 Km. The speed of light inside the link is at 2 × 108 m/s. The link has a bandwidth of 6 Mbps. Which component of the total delay is dominant? Which one is negligible? 7. Suppose that a digitized TV picture is to be transmitted from a source that uses a matrix of 480 × 500 picture elements (pixels), where each pixel can take on one of 32 intensity values. Assume that 30 pictures are sent out per second. Calculate the source data rate. 8. A digital signaling system is required to operate at 9600 bps. If a signal element is encoded into a 40bit word, what is the minimum required bandwidth of the channel? 9. Suppose that the spectrum of a channel is between 3 MHz and 4 MHz, and the SNR value in dB is 24. What is the maximum channel capacity?