ENEL700 Project 2020 S2 Copyright @ Jack Xuejun Li Auckland University of Technology 1 of 2 ENEL700 Project Instructions: This project (total 50 marks) contributes 50% towards your final grade of this paper. All work MUST be typeset using a word processor such as Microsoft Word with necessary figures, tables, flowcharts, equations and references. Matlab code should be included as an appendix. You are allowed to discuss the problems with your colleagues, but you MUST submit your own work. Turnitin will be used to check for plagiarism. Due Date: Monday 12 October 2020, 4pm. Part A. This part is on the quantisation of the signal ( ) sin , 0 t 10s t t= ≤ ≤ . Consider a sampling interval Ts and three different quantisation resolutions. (Total 35 marks) (1). Plot s(t) in a figure with the following sampling intervals: Ts=2s, Ts=1s, Ts=0.5s and Ts=0.1s. Use different line styles to differentiate them. Compare them and discuss the effect of sampling interval on the plot. (Hint: you may discuss the Nyquist Theorem and see how it works) (5 marks) (2). With Ts=0.1s, consider a 2-bit uniform quantisation process, answer the following questions: (a) what will be the quantisation interval Δ? (1 mark) (b) What is the maximum quantisation error? (1 mark) (c) What are boundary values for the quantisation intervals? (2 marks) (d) For sample collected at t = 0.3s, what is the associated quantisation error? (2 marks) (e) Calculate the mean square quantisation error. (2 marks) (f) Calculate the SQNR for the output of this quantiser. (2 marks) (3). With Ts=0.1s, consider a 3-bit uniform quantisation process, answer the following questions: (a) what will be the quantisation interval Δ? (1 mark) (b) What is the maximum quantisation error? (1 mark) (c) What are boundary values for the quantisation intervals? (2 marks) (d) For sample collected at t = 0.3s, what is the associated quantisation error? (2 marks) (e) Calculate the mean square quantisation error. (2 marks) (f) Calculate the SQNR for the output of this quantiser. (2 marks) (4). Consider Ts=0.1s, plot s(t) and its quantised signal copies using (a) 3-bit uniform quantiser and (b) 4-bit uniform quantiser in the same figure with the following line styles: red solid line with star markers (e.g., ‘r-s’) for the original signal s(t), black dashed line with circle marker (e.g., ‘k--o’) for 3-bit quantiser output and blue dotted line with square markers (e.g., ‘b:o’) for 4-bit quantiser output. (Hint: you may use the Matlab function quantiz and assume ENEL700 Project 2020 S2 Copyright @ Jack Xuejun Li Auckland University of Technology 2 of 2 Vp=C). NOTE: Please include your Matlab code and the figure in the solution. (10 marks) Part B. This part is on binary phase shift keying (BPSK). Consider the transmission of a random binary sequence data [1 0 1 1 0 0 1 1 1 0] using BPSK. (Total 15 marks) (1). The original data sequence is used to modulate a carrier signal. The modulated BPSK signal is shown in Figure 1(c). Comment on the plot in Figure 1(c) against the data in Figure 1(a) and the carrier signal in Figure 1(b). If Quadrature Phase Shift Keying (QPSK) is used, what are the main changes in the modulated signal wave as compared to that of BPSK? (5 marks) (a) (b) (c) Figure 1. (a) binary sequence (b) carrier signal (c) modulated BPSK signal (2). As shown in Figure 2, if Additive White Gaussian Noise is considered, the received BPSK signal is corrupted by in-phase noise. Comment on the waveform in Figure 2 as compared to the modulated BPSK signal in Figure 1(c). Explain what will happen to the received BPSK signal if phase delay is caused by the transmission medium. (5 marks) Figure 2. received BPSK signal (3). Theoretically, the bit error rate (BER) performance of BPSK is given by ( ) 2 0 2 2, where tbBPSK x E BER Q Q x e dt N x ∞ − = = ∫ and 0 b b E C B N N R = where C and N are the carrier power and noise power, respectively. B is the signal bandwidth and Rb is the data rate in bits per second1. Using Matlab function erfc to plot the BER performance for BPSK with 0 bE N in the range of [0dB 12dB] with a step size of 2dB. Comment on the result. (5 marks)
1 Please refer to this article: https://en.wikipedia.org/wiki/Eb/N0 0 0.5 1 Am pl itu de Original Binary Data 1 2 3 4 5 6 7 8 9 10 Time 0 1 2 3 4 5 6 7 8 9 10 Time -1 0 1 Am pl itu de Carrier Signal 0 1 2 3 4 5 6 7 8 9 10 Time -1 0 1 Am pl itu de Modulated BPSK signal 0 1 2 3 4 5 6 7 8 9 10 Time -2 0 2 Am pl itu de Received BPSK Signal 欢迎咨询51作业君
