HW

3.13 a. Suppose that a digitized TV picture is to be transmitted from a source that uses a matrix of 480 x 500 picture elements (pixels), where each pixel can take on one of 32 intensity values. Assume that 30 pictures are sent per second. (This digital source is roughly equivalent to broadcast TV standards that have been adopted.)
Find the source rate R (bps).

(30 pictures/s) (480 × 500 pixels/picture) = 7.2 × 106 pixels/s
Each pixel can take on one of 32 values and can therefore be represented by 5 bits:
R = 7.2 × 106 pixels/s × 5 bits/pixel = 36 Mbps

b. We use the formula: C = B log2 (1 + SNR)
B = 4.5 × 106 Hz = bandwidth, and
SNRdB = 35 = 10 log10 (SNR), hence
SNR = 1035/10 = 103.5, and therefore
C = 4.5 × 106 log2 (1 + 103.5) = 4.5 × 106 × log 2 (3163)
C = (4.5 × 106 × 11.63) = 52.335 × 106 bps

c. Discuss how the parameters given in part (a) could be modified to allow transmission of color TV signals without increasing the required value for R. 10 × 3 = 30 levels for each pixel element

3.15 What is the channel capacity for a teleprinter channel with a 300-Hz bandwidth and a signal-to-noise ratio of 3 dB, where the noise is white thermal noise?
W = 300 Hz (SNR)dB = 3
SNR = 100.3
C = 300 log2 (1 + 100.3) = 300 log2 (2.995) = 474 bps

3.16 A digital signaling system is required to operate at 9600 bps.
a. If a signal element encodes a 4-bit word, what is the minimum required bandwidth of the channel?

Log2 M = 4
C = 9600 = 2B × 4, and B = 1200 Hz

b. Repeat part (a) for the case of 8-bit words.
9600 = 2B × 8, and B = 600 Hz