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Short Questions:
- Differentiate between guided media and unguided media.
- Differentiate between an analog and a digital electromagnetic signal.
- What are three important characteristics of a periodic signal.
- What is the relationship between the wavelength and frequency of a sine wave.
- Define fundamental frequency.
- What is the relationship between a signal's spectrum and its bandwidth.
- What is attenuation?
- Define channel capacity.
- What key factors affect channel capacity?
Problems:
- Figure 1 shows the frequency domain function for a single square pulse. The signal pulse could represent a digital 1 in a communications system. Note that an infinite number of higher frequencies of decreasing magnitudes is needed to represent the single pulse. What implication does that have for a real digital transmission system?
2.(.)a Suppose that a digitised TV picture is to be transmitted from a source that uses a matrix of 480 x 500 picture eleme nts (pixels), where each pixel can take on one of 32 intensity values . Assume that 30 pictures are sent per secon
d. (This digital source is is roughly equivalent to broadcast TV standards that have been adopted.) Find the source rate R (bps) 2.(.)b Assume that the TV picture is to be transmitted over a channel with 4.5Mhz bandwidth and a 35dB signal-to -noise ratio. Find the capacity of the channel (bps). 2.(.)c Discuss how the parameters given in part (a.) could be modified to allow transmission of colour TV signals without increasing the required value for R.
- What is the channel capacity for a teleprinter channel with a 300Hz bandwidth and a signal-to-noise ratio of 3dB, where the noise is white thermal noise?
- A digital signalling system is required to operate at 9600bps. 4.(.)a If a signal element encodes a 4-bit word, what is the minimum required bandwidth of the channel? 4.(.)b Repeat part (a.) for the case of 8-bit words.
- Given the narrow (usable) audio bandwidth of a telephone transmission facility, a nominal SNR of 56dB (400,000), and a certain level of distortion, 5.(.)a What is the theoretical maximum channel capacity (kbps) of traditional telephone lines? 5.(.)b What can we say about the actual maximum channel capacity?
- Given a channel with an intended capacity of 20Mpbs, the bandwidth of the channel is 3MHz. Assuming white thermal noise, what signal-to-noise ratio is required to achieve this capacity?
- If an amplifier has a 30dB voltage gain, what voltage ratio does the gain represent?
- An amplifier has an output of 20W. What is the output in dBW?
there will be some distortion because of the loss of higher frequencies, the shape of the original pulse is known (by the specifications for the transmission system). Thus, the receiver will usually be able to distinguish a binary 0 from a binary 1.
4.(.)c (30 pictures/s) (480 × 500 pixels/picture) = 7.2 × 10 6 pixels/s Each pixel can take on one of 32 values and can therefore be represented by 5 bits: R = 7.2 × 10^6 pixels/s × 5 bits/pixel = 36 Mbps 4.(.)d We use the formula: C = B log 2 (1 + SNR) B = 4.5 × 10^6 Hz = bandwidth, and SNRdB = 35 = 10 log 10 (SNR), hence SNR = 1035/10^ = 10 3.5, and therefore C = 4.5 × 10^6 log 2 (1 + 10 3.5) = 4.5 × 10 6 × log 2 (3163) C = (4.5 × 10^6 × 11.63) = 52.335 × 10 6 bps
4.(.)e Allow each pixel to have one of ten intensity levels and let each pixel be one of three colors (red, blue, green) for a total of 10 × 3 = 30 levels for each pixel element.
- (^) Using Shannon's equation: C = B log 2 (1 + SNR)
We have W = 300 Hz (SNR)dB = 3 Therefore, SNR = 100. C = 300 log 2 (1 + 100.3) = 300 log 2 (2.995) = 474 bps
- Using Nyquist's equation: C = 2B log2M We have C = 9600 bps 4.(.)a log 2 M = 4, because a signal element encodes a 4-bit word Therefore, C = 9600 = 2B × 4, and B = 1200 Hz 4.(.)b 9600 = 2B × 8, and B = 600 Hz
5.(.)a Using Shannon’s formula: C = 3000 log 2 (1+400000) = 56 Kbps 5.(.)b Due to the fact there is a distortion level (as well as other potentially detrimental impacts to the rated capacity, the actual maximum will be somewhat degraded from the
theoretical maximum. A discussion of these relevant impacts should be included and a qualitative value discussed.
- C = B log 2 (1 + SNR) 20 × 10^6 = 3 × 10 6 × log 2 (1 + SNR) log 2 (1 + SNR) = 6. 1 + SNR = 102 SNR = 101
- For a voltage ratio, we have NdB = 30 = 20 log(V 2 /V^1 ) V 2 /V 1 = 10 30/20^ = 10 1.5^ = 31.
- Power (dBW) = 10 log (Power/1W) = 10 log20 = 13 dBW
