ES3C5: Signal Processing
Lab Assignment 3 Briefing Sheet
Submission Deadline: 12pm Noon on 5 December 2019
Module Leader: Dr Adam Noel D205, adam.noelwarwick.ac.uk Autumn 2019
1 Purpose
The following module learning objectives are applicable for this assignment:
Model signals, filters and processes using computer packages.
Design signal processing systems.
Apply signal processing systems to classify signals and extract information.
The focus of this assignment is signal estimation as an application of signal processing. You will find that the material from Lectures 21 and 22 and Lesson 18 in the notes is particularly relevant, though a general understanding of earlier module material is also helpful, including Lecture 20 Lesson 17 on random signals and our coverage of FIR filters.
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General Instructions
While it is expected that you may discuss the assignment with your classmates, your sub mission must be your own. Plagiarism of any kind is not acceptable and can result in a mark of zero.
Download the zip directory ES3C51920lab3data.zip from the ES3C5 Assessment and Feedback Moodle page. Extract three files: ES3C51920lab3template.m, uIDLab3signals.mat and IDLab3.txt, where ID is your student number.
Rename the file ES3C51920lab3template.m to uIDLab3.m where ID is your stu dent number and place that file and uIDLab3signals.mat in your MATLAB working directory this should be a directory where you have write privileges on your computer.
Open uIDLab3.m and rename the function title in the first line from ES3C51920lab3template to uIDLab3 where ID is your student number. Do not change the output argument Answers or any of the code in the toplevel function. You will be entering all of your code in the subfunctions. Also, do not change the output arguments of the subfunctions or introduce any new input arguments.
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Complete the problems listed in Section 3 and refer to IDLab3.txt for the parameter values that you must use. You will also need to load data from uIDLab3signals.mat, and there are already calls to do this as needed in the template code. Enter the required code for each problem in the corresponding subfunction in uIDLab3.m. The code must calculate the answers using your assigned parameters and data set unless otherwise indicated. When a question includes plotting a figure, the corresponding plot call must be included inside the subfunction code, but details such as axis labels and legends can be added after your solution function runs.
ALL plots must be labelled with suitable axis and curve labels. There are points specifically allocated for this. Include your student number and the question number in each plot title. Each plot shall be saved as a jpgfile where the filename is the number of the question.
Include readable comments in your code that briefly summarise your steps. See the subfunc tion Q0 below and in uIDLab3.m as a template example with suitable comments:
function c0 Q0
Assign answer to c0 double value
Define triangle lengths
a0 2; 1st side
b0 1; 2nd side
Find length of hypothenuse
c0 sqrta02 b02; Pythagorean theorem to find 3rd side
end
Combine your code file uIDLab3.m with all of the saved figures into a single zipfile called uIDLab3.zip where ID is your student number. You must submit the zipfile to Tabula.
Problems
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Please answer all of the following questions with reference to IDLab3.txt for your specific parameter values and uIDLab3signals.mat for your data where applicable.
4 points 1 for each problem are allocated for providing suitable comments in your code that explain key steps and demonstrate your understanding of your implementation. However, suc cinctness is still appreciated.
1. 6 Points You work for Midlands Space and are helping to monitor a series of test rocket launches that will be used to install navigation satellites. You are assessing the performance of a timeofflight sensor that will be used to help measure the rocket altitude. You have collected a series of noisy altitude data and you wish to fit the data to the quadratic function
ytA1 B1tC1t2 wt, 2
such that you need to estimate the parameters A1, B1, and C1 you do not need to worry about the units of these parameters and w t is a noise signal. Your data was collected starting from time t 0 at the constant interval defined in your parameter file. The noisy data vector y1 is provided in your data file uIDLab3signals.mat and there is already a call to load this vector in the Q1 subfunction. Please answer the following:
a Construct the linear model observation matrix O to estimate the unknown parameters A1, B1, and C1. Assign O to Q1 subfunction output argument O1.
b Apply linear model estimation to estimate the unknown parameters A1, B1, and C1. Assign these three constants in the same order to the 31 Q1 subfunction output vector param1.
c Use the parameter estimates to predict the altitude data for the same times at which the sensor values were taken. Compare the predictions with the actual sensor values in a timedomain plot treat the yaxis as altitude in metres. Save the plot as a jpgfile named Q1.jpg. Calculate the mean square error of the predicted values and assign this error to Q1 subfunction output argument mse1.
2. 6 Points You are a control engineering consultant and are visiting the factory of the XYZ Manufacturing company to test an industrial heating system. Based on the system specification, you expect the impulse response to behave according to the general equation provided in your parameter file where w t is the noise signal. You have collected noisy thermometer readings but a poor uplink from your sensor meant that many readings were dropped and you only have recordings y2 for the times given by the vector tVector2 both provided in your data file uIDLab3signals.mat. Please answer the following:
a Construct the linear model observation matrix O to estimate the unknown parameters A2, B2, and C2. Assign O to Q2 subfunction output argument O2.
b Apply linear model estimation to estimate the unknown parameters A2, B2, and C2. Assign these three constants in the same order to the 31 Q2 subfunction output vector param2.
c Use the parameter estimates to predict the temperature for the same times at which the sensor values were taken. Compare the predictions with the actual sensor values in a timedomain plot treat the yaxis as arbitrary temperature. Save the plot as a jpgfile named Q2.jpg. Calculate the mean square error of the predicted values and assign to Q2 subfunction output argument mse2.
Hint: This is intended to be a challenging problem, but we have covered all of the material that you need to solve this problem in Lecture 21 Lesson 18. Note that you do not have a fixed sampling interval here. Also, the lectures and module notes state that our signal can include polynomial terms of the function variables. This generalises even further; our signal can include practically any function of the variables, as long as the signal is linear in the unknown parameters.
3. 6 Points You work for ACME Mobile and you are performing wireless propagation testing in Coventry where a new 5G base station will be installed. Since there are many cloudy days, you are measuring the impact of signal reflections when the base station is communicating with a mobile user. You have worked out that there are two primary signal paths of interest:
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the direct path from the base station and one that reflects off of the clouds. The reflected cloud signal arrives 2 samples later than the direct signal. Thus, you can write the received signal as a noisy difference equation of the form:
y n A3x n B3x n 2 w n .
You have collected samples of the received signal y n based on the transmission of a pseudo random pilot sequence x n, and these are given as the vectors y3 and x3, respectively, in your data file uIDLab3signals.mat. The noise signal is w n. Please answer the following:
a Construct the linear model observation matrix O to estimate the unknown parameters A3 and B3. Assign O to Q3 subfunction output argument O3.
b Apply linear model estimation to estimate the unknown parameters A3 and B3. Assign these two constants in the same order to the 21 Q3 subfunction output vector param3.
c Use the parameter estimates to predict the received signal for the same pilot sequence. You do not need to save a plot. Calculate the mean square error of the predicted values and assign to Q3 subfunction output argument mse31.
d Consider an alternative received signal model where you account for an additional re flected component that arrives 1 sample after the direct signal, i.e., the received signal is a difference equation of the form:
y n x n x n 1 x n 2 w n .
Repeat the estimation problem with these three unknown parameters and determine the corresponding mean square error with the same data set y3 and pilot sequence x3. Assign the mean square error to Q3 subfunction output argument mse32. Provide a brief 12 sentences comment on the significance of the difference if any between mse31 and mse32. Write this comment as a string to Q3 subfunction output argument comment3.
4. 6 Points You work for Healthy R Us Medical Devices and you are testing a new batch of EEG sensors for recording electrical brain activity. You have identified a sensor that appears to be particularly noisy and is reading strong values even when there is no connection. You have made a recording of values produced by the sensor and these are saved to y4 in your data file uIDLab3signals.mat. You wish to determine the probability distribution of the signal using maximum likelihood estimation. Please answer the following questions:
a Use the mle function to fit the sensor data to a continuous uniform distribution. Assign the lower and upper bounds of the estimated distribution to the 1 2 Q4 subfunction output argument param4Uni.
b Use the mle function to fit the sensor data to a Gaussian i.e., normal distribution. Assign the mean and variance of the estimated distribution to the 1 2 Q4 subfunction output argument param4Normal.
c Superimpose both estimated distributions on the empirical distribution of the data set. The empirical distribution is obtained by plotting the signal histogram and is included in the Q4 template code. The addition of your probability density curves without overwriting the histogram is enabled by setting the plots hold option on. Clearly
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distinguish and label all of the data e.g., using a legend. Save the plot as a jpgfile named Q4.jpg. Hint: We describe several useful probability density functions in Lecture 20 Lesson 17.
d Briefly comment 12 sentences on which distribution appears to be more accurate and why. No calculations are necessary. Write this comment as a string to Q4 subfunction output argument comment4.
4 Submission of Deliverables
You submit the zipfile uIDLab3.zip where ID is your student number that should contain: uIDLab3.m where ID is your student number
Q1.jpg
Q2.jpg
Q4.jpg
Be sure that uIDLab3.m runs correctly with no other custom files required. You must submit
the zipfile to Tabula.
Your assignment must be submitted by 12pm noon on Thursday 5 December 2019, otherwise late penalties will apply.
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Marking Criteria
problem will be marked according to:
Correctness of the answers and figure contents.
Calculations and labelled plots used to arrive at the answers. Code running efficiently as expected.
There is a total of 24 points available. This includes 4 points allocated for providing suitable comments in your code.
6 Assignment Weighting
This assignment is worth 10 of your module mark.
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