1). a). A discrete source produces the symbols 0 and 1. Is source encoding necessary, discuss?
b). A discrete symbol generator produces five symbols A, B, C, D and E with the respective probabilities 0.9, 0.05, 0.03, 0.01 and 0.01 respectively.
i). Encode the symbols in part (a) using fixed length encoding using the minimum number of bits per symbol and determine the coding efficiency.
ii). Use the code word distribution 1, 01, 001, 0001 and 00001 and compare with the efficiency in i).
iii). Discuss the implications of using such a coding method on relevant system parameters.
c). A binary symmetric channel was tested by communicating 106 1's and 106 0's during this period it was found that four 1's were received incorrectly and four 0's were received incorrectly. The channel is then used with a source that generates 9000 1's out of a total of 1.5×105 bits. Sketch the symmetric channel (channel probability diagram) labelling with actual values state any assumptions made.
Explain what the diagram is depicting and how it can be used for efficient communication of messages.
2). Consider the following three waveforms.
a). i). Explain how plot 3 is formed with respect to plots 1 and 2 including relevant equations.
ii). Determine the modulation index.
b). A sine wave Vm(t) is given by Vm(t) = sin(2×?×1×t). A square wave Vc(t) has a frequency of 8Hz and high and low values of -1 and +1 (duty cycle is 50%).
i). Sketch the sine wave for one time period.
ii). Sketch the square wave for one time period.
iii). Sketch the output y(t) from the block diagram , Figure Q 2 b)., for an offset of 0 V.
iv). Sketch the output y(t) from the block diagram , Figure Q 2 b)., if now the high and low values of the square wave are 0 and +1 and the offset, is 0 V(duty cycle is 50%).
v). Explain with reference to appropriate mathematics how this can be viewed as analogue amplitude modulation and practically how the analogue amplitude modulated signal can be obtained.
3). An FM transmitter has a carrier frequency of 150 MHz. The modulating signal is a 1 kHz sine wave, and the deviation is set at 2 kHz.
i). State the frequencies of the sidebands produced and draw a fully labelled and scaled amplitude frequency spectrum of the transmitter output.
ii). Outline the working principles of a voltage controlled oscillator (VCO) and show a fully labelled graph of the oscillation frequency vs DC voltage obtained from your experimental data during the laboratory on frequency modulation. Comment on the linearity of the VCO.
iii). Explain the significance of the zero crossings on the Bessel function graphs and how they can be used to provide information about an FM transmitter.
4). i). A two level amplitude shift keying scheme (ASK) is implemented by multiplying square pulses of 1 microsecond duration (non return to zero) and amplitudes 1 and 5 V with a sinewave of frequency 5MHz and amplitude 1 V. Sketch the two possible modulated waveforms (for a low and a high) and state the data rate. Suggest what bandwidth the modulated signal would require giving reasons for you answer.
ii). Sketch a constellation diagram for a modulation scheme that is represented by the four symbols:
Asin(ωt) for a 11
Asin(ωt + 90o) for a 01
Asin(ωt + 180o) for a 00
Asin(ωt + 270o) for a 10
where A is represented by the following shape with T0 equal to the symbol period.
