Signals and Systems (10 credits) Final Project Academic Year 2019/20
Goals of the Final Project
The Final Project has the following goals:
1. develop critical thinking: the student should be able to understand if the obtained result (either theoretical or measured through a suitable computer program) is realistic/reasonable or not
2. improve the ability of writing reports: the student should practice this ability
3. develop the ability of the student to correctly/reasonably set unknown parameters
Therefore, the project is not described with all the details (you have to make your choices and justify them). On the other side, it is required that you get your results in two or more different ways in order to check that they are correct and find potential errors (critical thinking). The report must include the description of all the required activity, in many cases it is expressly said what the report must include, in other cases it is left to you to decide what to write and how to show your results. Take your responsibility.
Who has to complete the project
The project must be carried out by students who are attending Signals and Systems with 10 credits, in particular students of the Electronic and Communications Engineering (ECE) Bachelor Degree. They have to write the Matlab code and the report that comments the results. The maximum grade of the report is 30, this grade will be combined with the grades of the written and (optional) oral parts to give the final grade of the exam. ECE students have Signals and Systems attached to class Final Project (1 credit): the grade of Signals and System will be copied as grade of Final Project by the registrar’s office.
Each student shall write his/her own report. Plagiarism will result into suspension. Deadlines
The report must be uploaded in folder ”elaborati” on the course web-page by
January 20th 2020 (11.59 PM);
intermediate reports are not required. The report must be a unique pdf file with filename yoursurname sxxxxxx SaS 2019 20.pdf,
(where xxxxxx is your id – matricola – number) that also includes the Matlab script in the appendix. The maximum length of the document is 6 pages (not including the Matlab script).
It is not possible to sit the exam without the report.
YOU MUST UPLOAD THE FILE BY JANUARY 20th 2020, whatever is its content. If you did nothing, you have to upload just the first page of the report with your name, id number (matricola), class, academic year, the filename must be as described above.
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Minimum requirements for writing the report
• Thereportmusthaveafirstpagewiththetitle(SignalsandSystemFinalProjectReport,Academic Year 2019/20), the author, the id number (“numero di matricola”).
• All the pages (apart from the very first) of the report must be numbered, you must justify the text. Maximum number of pages: 6; font: Times New Roman, 12 pt, line spacing: single, page format A4: margins 2 cm right, left, top and bottom.
• The report must be organized in sections and subsections.
• Youmustdescribethegoaloftheproject,thereportmustbeself-standing,itshouldbecompletely understood by a professor of Signals and Systems who teaches in another university (you must explain the notation you used, you don’t need to explain what the FFT is). Assume that this professor never read the file you are reading now, and he knows nothing about tasks 1, 2, 3 described, respectively, in Sections 4, 5, 6).
• Usethespellchecker,readyourreportatleast3timestoremovethegrammarerrors(missing“s”, wrong use of articles, etc); if you are not sure about the use of a word, check it.
• Avoid using “I” in the report, it is not professional.
• The figures in the report must be numbered and must have a caption (note: the title of the figure you specify in the Matlab script is NOT the caption). The caption of figure must be below the figure, next to the figure number.
• In the report you must refer in the text to all the figures included in the report, and you must use the number of the figure (i.e. don’t write “In the figure below” but “In figure 3.2”).
• The plots must include the labels on the axes and the grid.
• The scale in the plots must be such that the plots are clearly readable.
• You are responsible of choosing if the x and/or y data are represented in a logarithmic scale or in a linear scale, and you must choose the most appropriate one.
The quality of the report must be that of a technical book written by a professor.
We suggest that you use Latex for writing the report, but it is not mandatory. In any case you must provide a pdf file, the Matlab scripts must be included as text in the appendix. Once you obtain the final Matlab script and you get the correct results, immediately write the report, don’t wait till the last useful day. Writing the report takes time. Once you have your report, check again the list above, in case you
forgot one of the requirements.
2 Requirements for writing the Matlab script
You can only use basic functions of MATLAB, you cannot use Simulink, you cannot use Matlab
symbolic math. Allowed Matlab functions:
• Operators: +,-,/,*,^, <,>,<=,>=,=~,==, etc
• Special symbols: 1j, pi
• Functions: log, exp, log10, abs, real, imag, floor, ceil, mean, var, std, length, audioread, audioinfo, play, fft, fftshift, ifft, ifftshift
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• Functionsneededtogeneratefigures:figure,plot, semilogy, semilogx, loglog, grid, xlabel, ylabel, hold, legend, axis, etc
• Statements: if, else, for, end, while, switch, case, etc 3 Task 0 of the project – no points
Implement and check the correct working of a PLL: the input signal is the complex envelope of a pure carrier at frequency fc = 101 MHz, with phase φTX = 40 deg and power 1. Simulate 105 samples at sampling frequency 44.1 kHz; set the value of the learning coefficient γ so that the PLL correctly estimatesφTX in10-20thousandsamples.
4 Task 1 of the project – 20 points
Task 1 aims at the simulation in Matlab of a DSB transmission system with residual carrier, in the absence of noise and Doppler effect. It is convenient to work step by step, separately analyzing the correct working of each subsystem.
1. Findamusicpieceofaround100s(ortakeaportionofaround100sofalongerpiece)in.wavfor- mat. Write a Matlab script that uploads the music signal x(t) (.wav file) using function audioread. Initially work on a subset of around 100 thousand samples (use parameters START/STOP of au- dioread); when the Matlab program runs correctly, use the entire file and give the final results and plots for the entire input file. The report must include a description of the input file (you must specify the sampling frequency, overall duration of the signal, title of the music piece, etc). Don’t include the .wav file in the uploaded material, your code will be checked with another wav file. Plot in two separate figures the left and rights channels (complete signal).
2. Evaluate the average power Px of the signal in the simulation time interval (the sum of the power of xR(t) and that of xL(t)). NOTE: the code lines to evaluate Px must be part of the script (i.e. don’t write in the script directly Px=10, but measure the power so that the script can run with another music piece).
3. Generatethecomplexenvelopex ̃TX(t)oftherealtransmittedsignal xTX(t) = [Ac +xR(t)]cos(2π fct +φTX)+xL(t)sin(2π fct +φTX)
being φT X = 40 degrees. Set the amplitude Ac of the residual carrier so that the residual carrier power is 20 dB lower than Px.
4. Generate the complex envelope y ̃RX(t) of the received signal yRX(t). In Task 1, there is no noise nor Doppler effect, so simply set y ̃RX (t ) = x ̃T X (t ). Note that in task 2 y ̃RX (t ) will be different from x ̃ T X ( t ) .
5. Signal yRX(t) should be directly the input of the PLL, but the synchronizer might not work cor- rectly with this input. Even if a carrier exists, the DSB signal behaves like noise for the PLL and makes the phase recovery more difficult. It is necessary to remove most of the interfering DSB signal by an appropriate bandpass filter, in real life, which corresponds to a low-pass filter when working with complex envelopes. To reduce the burden of the project, you are not required to simulate a low-pass filter: simply evaluate the FFT of the entire signal y ̃RX(t) and appropriately multiply it by the transfer function of an ideal low-pass filter with bandwidth around 20-30 Hz, then appropriately use the IFFT to get signal y ̃FIL(t) in the time domain. Check the FFT of y ̃FIL(t).
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Then normalize y ̃FIL(t) so that it has power equal to 1 (you go back to the conditions in which you tested the PLL in task 0).
Plot the estimated phase versus time and check that the final value is correct. The report must specify the chosen value of the phase update parameter γ, the plot of the estimated phase (deg) versus time, the plot of the estimation error (deg) (estimated phase minus ideal phase).
6. Generate the demodulated signals xˆR(t) and xˆL(t), and compare them with xR(t) and xL(t) in two plots; also plot the reconstruction error (i.e. the difference between the modulating signal and the received signal). The plots of the errors must be included in the report.
The report must include your comments on the obtained results.
5 Task 2 of the project – 5 points
Repeat Task 1, but this time simulate a Doppler effect. Assume that the DSB receiver is on a car that moves away from the transmitting antenna at a constant speed equal to 120 km/h (initial distance: 10 km). Assume that the center frequency fc of the TX signal is 101 MHz. Assume, for simplicity, that there is no attenuation on the channel. The report must include the same figures described in Task 1 (apart from item 1). Listen to the demodulated signal. Add your comments.
6 Task 3 of the project – 5 points
Change (reasonably) the value of parameter γ in task 1 and in task 2 and, for each value of γ, measure the signal to noise ratios for the demodulated signals:
SNRL = E{xL2(t)} E{[xL(t) − xˆL(t)]2}
SNRR = E{xR2(t)} E{[xR(t) − xˆR(t)]2}
Include in the report a table with the values of SNR (dB) and the corresponding values of SNRL (dB) and SNRR (dB). Write your comments on these results.
7 Final checks
The report must include 10 plots (2 plots of the input left and right channels, 4 plots for task 1, 4 plots for task 2) and 1 table.
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