EEEN30160 Real Discrete Time Signals and Mathematical Functions in MathLab

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Must be done in Matlab R2019B. every thing is described on the PDF.

A description on the process done to achieve the solutions and graphs must be provided on a Microsoft word document

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EEEN30160: Matlab Exercise 1 General Guidelines: • Remember to put your Student Number on the report • Remember to put the name of your partner in the report • For each exercise generate a script (.m file) with all the commands, that will be uploaded together with your report. Some exercises will specifically request additional functions to be generated and called from the main script. Upload also the functions when requested by the exercise. • Remember to label (both x and y axes) your graphs. In the labels put also the measurement unit in parenthesis (e.g. seconds or samples for time axes). For arbitrary signals use (A.U.), meaning Arbitrary Units, as measurement unit. Points will be subtracted from the score of each exercise for any missing label. • COMMENT YOUR CODE. A perfect code with no comments will count for half of the points assigned to the exercise. • Each exercise is worth the same number of points • THE WORK IS DONE IN PAIRS BUT EACH STUDENT SHOULD SUBMIT HER/HIS OWN REPORT Handling and plotting theoretical and real discrete-time signals and mathematical functions in Matlab Matlab provides a user-friendly programming environment with great flexibility, very well-suited to modeling, analyzing physiological data and developing biomedical signal processing algorithms. In this lab we will become familiar with handling and plotting discrete-time signals in the Matlab environment – both theoretical signals we generate with equations, and real data. Part I: mathematical function plotting Say you want to generate a sinusoid of a certain frequency, and plot it. Matlab, not being a live thinking entity, has no clue what you want to do so you need to specify EVERYTHING to it. Let’s say you want to plot a 5-Hz sinusoid over a 2-second time frame beginning at 0. We want it to have an amplitude of 2 and have a cosine phase (begins at its peak/maximum at time 0). We are trying to construct a signal that is a function of time, so we should therefore define ‘time.’ And it’s a discrete-time signal so we need a value of the signal only at discrete – usually evenly-spaced – times. Let’s choose a ‘sampling rate’ of 200 Hz, in other words, choose to evaluate the function in discrete 5-ms steps: >> t = [0:0.005:2]; % define ‘time’ in seconds Now that we’ve defined a discrete time-base, let’s evaluate our desired function at these times to generate our signal: >> f = 5; % define frequency of sinusoid as a parameter, in Hz >> my_signal = 2*cos(2*pi*f*t); % our cosine Now, plot your signal against time: >> plot(t,my_signal) It looks nice and smooth, as if it were continuous. But it’s not - it’s discrete, but has a fine enough sample rate that it appears continuous. To see this, use the ‘stem’ function instead of ‘plot’ and zoom in to take a closer look – it’s just a series of discrete numbers. Problem 1: write a function that generates and plots a cosine as above, which takes the following arguments (input parameters) and produces the following outputs: function x = plotsinusoid(f,a,startT,endT,step) where f is the frequency of the cosine, a is the amplitude, startT and endT the start and end times in sec, and step gives the sample period (reciprocal of sampling rate). x is the generated cosine signal. As a hint to see how functions work, here is a two-line m-file ‘expsig.m’ that generates (although doesn’t plot) an exponential signal for a series of integers n running from 0 to N-1: … It’s that simple! NOTE: THE M-FILE SHOULD BE SAVED UNDER THE SAME NAME AS THE FUNCTION Use the functions xlabel and ylabel to give the axes labels – ‘Time (sec)’ and ‘Amplitude’. Run the function from the command line with parameters f,a,startT,endT,step of your choosing (different from above), and reproduce the command and resultant plot in your report. IMPORTANT: make a folder on your computer to contain all the files you will make, and GO THERE in Matlab. Before you leave SAVE everything from that folder on a memory stick or email it to yourself. Problem 2: In signal processing we use complex exponentials to represent sinusoids because they can represent both the phase and the amplitude of the sinusoid in their angle and modulus, respectively. Recall Euler’s formula: Now write a new function ‘plotsinusoid2.m’ that takes the SAME input arguments as ‘plotsinusoid.m’ but outputs the sinusoid x in complex exponential form instead. Also, have it produce TWO figures: in the first (shown on right), plot the real part of x, the imaginary part of x and the modulus of x in the same axes. In the second plot the angle in DEGREES with the same time-base. Label all axes in all plots. Again reproduce the command and plots in your report. You will find the matlab functions exp, real, imag, abs and angle useful. To make a new figure in matlab and enable plotting of multiple traces in that figure, use figure; hold on Part II: loading and plotting physiological data Problem 3: Download the file ‘EvokedPotential.mat’ from Brightspace and put it in your working folder (your ‘current directory’ in Matlab). This mat file contains a single vector of the same name, which is a hypothetical electrical signal recorded from the scalp using electroencephalography (EEG), which was evoked by a beep that was played in the subject’s ear. This subject is suspected to have multiple sclerosis (MS), and to aid in diagnosis, you are asked to determine the post-beep time in milliseconds at which the FIRST POSITIVE PEAK occurs. This latency tends to be longer in individuals with MS, averaging around 150 ms compared to around 120 ms in neurologically healthy people. You are told that the ‘epoch’ or time frame of this record extends from -100 ms (i.e., 100 ms BEFORE the beep event) to +650 ms, where the 0 ms point coincides with the beep onset. Load EvokedPotential.mat into the workspace. From the information above, determine the correct timebase that the evoked potential should be plotted against, and plot it. By zooming in the figure, determine by eye the time, in MSEC RELATIVE TO THE BEEP, at which the first positive peak occurred. Provide the plot, the peak latency and the code used in your report. How would you diagnose this subject, and why? Part III: basic programming in matlab Problem 4: The Root Mean Square of a discrete-time signal is given by We can easily calculate the RMS of signals in MATLAB using a combination of the sum, sqrt, and ^ commands. N represents the number of samples of the signal. Please note that the command .^ applied to a vector squares each element of the vector. Write a script to calculate the RMS of the discrete-time signal x, defined as follows: n = a vector of number between -10 and 10 with increments of 1. x = n/3 + n3 There is a function that calculates the rms in matlab (rms) compare the results of your formula with that of the native function Problem 5: Averaging. This technique is very useful for de-noising periodic signals (of known period) or event-locked quasi-deterministic signals when the signal and the noise are uncorrelated. Generate a 100 seconds cosine with a frequency of 5Hz, using 100 samples per second (starting from the instant 0.01). Each second of the sinusoid signal represents one epoch. Now generate a vector of white noise, of the same length as the cosine, using the function rand (amplitude = 3); Plot the 12th epoch of the noisy signal. Use a for loop to generate and plot a signal that is the average of all the epochs in the first 10 seconds of the signals (thus the first 10 epochs). Then use another for loop to generate and plot a signal that is the average of all the epochs in the 100 seconds of the signal. Present and comment the plots on your report. the cosine epochs Upload your report including all plots and WELL-COMMENTED code to blackboard by Thursday October 3.
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Here is the Matlab code and report, packaged into the zip file shall mark the job as complete. If you need modifications that are within the job description, I shall make them. I had to do some research ...

Really helped me to better understand my coursework. Super recommended.