ECM3166: COMMUNICATIONS ENGINEERING
Tutor Marked Assessment 1
This assignment carries 10% of the module mark. Completed work should be submitted as a single .pdf file via the submission point on ELE by 12 noon on 8 November 2024.
Q1 [40 marks]
(a) Complete the code table shown below (table Q1) for a 4-bit PCM system using natural binary, and an input voltage range of 0 to 1.5 V. [6 marks]
(b) Shown in Figure Q1 is an output waveform. generated from an analog input signal using the PCM encoding scheme in table Q1 and anAMI (bipolar RZ) line code. Re-construct (i.e. sketch) the sampled signal, along with the original analogue signal from which the AMI waveform. of Fig. 1 originates (assume that the signal is periodic with a period equal to 10 TS, where TS is the sampling interval). [18 marks]
(c) What is the frequency of the original analogue input signal? Has this signal been sampledata high enough frequency to avoid aliasing? [6 marks]
(d) The 4-bit PCM code words are now Hamming (7, 4) channel coded. Add an additional column to Table 1 showing the Hamming codewords for each of the PCM codewords. You must define the Hamming code and include working to demonstrate how you have calculated the Hamming codewords. [10 marks]
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Quantised signal amplitude (V)
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PCM codeword
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0
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0000
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0.1
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1.5
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1111
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Table Q1: PCM code table - the MSB is a sign bit.
Figure Q1: AMI line code waveform. representing a PCM-coded analogue input signal
Q2 [35 marks]
(a) Write down the standard equation for μ-Law compandingas used in PCM telephone systems and explain briefly why such companding is useful and/or necessary. [5 marks]
(b) Produce a simple program in Matlab/python to demonstrate the effects of this μ-Law companding on a 1 kHz sine wave having a peak amplitude of 1 V. Your program should be capable of calculating and plotting the input signal (the 1 kHz, 1 V sine wave) and the output signal after companding (by using the equation for the μ-Law). Plot, on a single graph, the compander output signals (over one complete period) for values of μ equal to 100 and to 255, along with the input signal. [25 marks]
(c) Calculate the approximate SQNR (in dB) for each of the above values of μ (assume an 8-bit system). [5 marks]
Q3 [25 marks]
Research and write a short discussion (maximum of 1 page) about the importance of data security and briefly describe one method of encryption used in modern digital communications.