1     General Instructions

Heads up regarding names: These  instructions  include precise case-sensitive  guidance regarding names of files, directories, functions, and variables. These must be followed exactly so that the marking scripts run correctly. There will be marks deducted for any deviations. Precise naming is standard practice in programming to ensure integration.

The instructions to complete this lab assignment areas follows:

1. Download the zip file ES3C5_2023_2024_lab_data_v2_1.zip (link)from the ES3C5 Moodle

Page under the Assessment Information heading. Extract four files from the zip file:

(a)  ES3C5_2023_2024_lab_template.m

(b)  ES3C5_2023_2024_lab_template.docx

(c)   u_lab.txt

(d)  ES3C5_2023_2024_lab_recording_v1_1.pdf

where is your student number.

2.    Download  your  signals  file   u_lab_signals.mat  from  the ES3C5   Coursework  Lab Assignment Signals Files page (link)under the Assessment Information heading, where  is your student number.

Note: This is a separate download so that you do not need to download everyone else’s signals (over 100MB).

3.    Rename the template files as follows:

ES3C5_2023_2024_lab_template.m  to   u_lab.m   (where     is  your  student number; don’tforget the “u” prefix here!) and place the file in your MATLAB working directory  (this  should  be  a  directory  where  you  have  write  privileges  on  your computer).

ES3C5_2023_2024_lab_template.docx to u_lab.docx.

4.    Open u_lab.m and        rename the  function        titlein    the  first        line from

ES3C5_2023_2024_lab_template() to u_lab() (where  is your student number). Do not change the output argument Answers or any of the code in the top-level function. Do not change the input or output arguments of the subfunctions.

5.    Completethe  prescribed   steps      in     the Recording    Supplement

(ES3C5_2023_2024_lab_recording_v1_1.pdf) to record the audio data that you will use to answer    the    problems    in    Question    1.    This     data    will    be    stored    to    the    file u_lab_Audio.mat.

6.    Complete  the  problems  listed  below  in  Section  6  and  refer  to  u_lab.txt  for  the functions and parameter values that you must use. You will need to load signals from u_lab_signals.mat and there are already calls to do this in the template code. Enter the required  code  in the  corresponding subfunctions in  u_lab.m; you  should  not write your own functions and you should only use functions from toolboxes that we cover in the module. The code must calculate the answers using your assigned parameters unless otherwise indicated. Take care to use parameters with the correct units.

7.    When a question includes plotting a figure, please account for the following:

(a)  Always start by creating a new blank figure. Do not close or overwrite existing figures.

(b)  The plot function calls must be inside the question subfunction code.

(c)  Carefully consider appropriate parameter ranges to view all necessary detail.

(d) ALL submitted plots must have labelled axes. You can add labels after your code runs.

(e)  Any data point label should include the parameter name, value, and units.

(f)   Figures must include your student number and question number at the top.

(g) ALL submitted plots must be placedinu_lab.docx as png images.

8.    Include readable comments in your code that briefly summarise your work, especially critical steps. See the subfunction Q0 in u_lab.masa template example.

9.    Run your code file from the MATLAB command line and write the output to a structure named Answers. Save Answers to amat filenamed u_lab_Answers.mat. For example, you can run your code as follows (remember to correct the apostrophes if copying):

Answers = u_lab; % Runs assignment code

save(’u_lab_Answers’, ’Answers’) % Writes output to file

10.  Place all necessary files into 1 folder named u_lab, and compress it into a single zip- file  called  u_lab.zip  (where    is  your  student  number).  Submit  the  zip-file to Tabula.

Be sure to place the files into the named folder before zipping. This ensures that your code is nested in its own subdirectory when unzipping.

2     Recording Supplement

Refer to ES3C5_2023_2024_lab_recording.pdf for instructions on recording and saving audio.

2.1     Specification of the Data to Record

The (imaginary) premise is that the University has decided to add voice codes as an option in two-factor authentication, so you can state the last 4 digits of your student number in order to access University systems. You will record your voice saying the last four digits of your student number.  This  recording  must  be  recorded  to  a single channel (mono) at  a sampling frequency of 22.05kHz and must be exactly 3 seconds long. If the original recording is longer than 3 seconds, then you must shorten it to 3 seconds before saving to u_lab_Audio.mat with the variable name audioRaw. Refer to ES3C5_2023_2024_lab_recording.pdf for additional guidance.

3     Questions (Total: 100 Marks)

Please answer all of the following questions with reference to u_lab.txt for your parameter values. All  code  to  solve the  following  problems  must  be  included  in  u_lab.m.  Written answers in u_lab.docx are required where specified, including copies of output figures.

25  marks are  designated  as  being  part  of “First Class Problems”.  These  questions  are deliberately more challenging. The instructors and lab demonstrators will not provide guidance on how to answer them. Clarifications can be made regarding what these questions are asking.

Up to 30 Marks in total can be deducted for poor coding style. Poor style includes:

Writing output to the command line (e.g., by omitting semi-colons for output suppression)

Insufficient   use   of   code    comments   to   explain   key   steps   and   demonstrate your understanding of your implementation. However, succinctness is still appreciated.

Here are the questions:

1. (30 Marks) This question concerns audio generation and processing. Please complete the following:

(a)  (4 marks) Complete the appropriate steps in the recording guidance and save your audio recording vector with the correct specification to the file u_lab_Audio.mat. It is needed to proceed with Question 1. Load the recording into the Q1 subfunction. The subfunction has template code that you just need to update.

Note: There  is  nothing to calculate here; this  part is being evaluated by the correctness ofyour audio and loading it into the a1 subfunction.

(b)  (6 marks) Your recording has become contaminated by a noise source. The contents

of the noise source are in the vector n1 in your signals file u_lab_signals.mat.

i.     Add the noise source vector n1 to your audio signal Q1.audioRaw. Assign the noisy signal to Q1.audioNoisy.

ii.   Calculate the fast Fourier transform (FFT) of Q1.audioNoisy. Do not apply scaling. Assign the FFT to vector Q1.FFT.

See the Extra box  14.2 “Double-Sided vs  Single-Sided  FFT” in the lecture notes to be aware that the MATLAB help examples present the FFT different from how you should calculate it. You must find the double-sided FFT (which we cover) and not the single-sided FFT (which we do not cover). iii. Plot the magnitude of this FFT output as a function of Hz frequency (i.e., a domain of [0,22050)Hz should be visible). Include a label for the largest noise frequency component. Save the FFT magnitude plot as a png file and include it in u_lab.docx.

(c)   (12 marks; “First Class  Problem”) Design an FIR filter to isolate (i.e., primarily output only) the largest noise frequency component.

i.     In no more than 4 lines of text in  u_lab.docx, describe and justify a target FIR filter performance specification. The specification should be sufficient to assess  a  candidate  design  by  inspection  of  the   magnitude  of  the   filter’s frequency   response.   Consider    practical   values   for   the   band    gains   and frequencies.

ii.   Design a filter that meets your target specification. Assign the filter impulse response to Q1.h.

iii.  Plot the frequency response of your design. You must use freqz as the plotting function. Use sufficient labels to verify your design. Save the plot as a png file and include it in u_lab.docx.

iv.  Briefly (in no more than 2 lines of text) explain in u_lab.docx whether your plot validates the design.

v.    Test your filter design. Pass your noisy audio signal Q1.audioNoisy through your designed   filter   using    the   filter    function.   Assign   the    filtered   output   to Q1.audioNoiseIsolated.

(d)  (8 marks) You wish to make your voice recording sound more interesting. Consider applying aflanging effect that adds a time-varying delay. You will use aflanging filter with the following time-domain difference equation:

y[n] = x[n] + Ax[n − 0.5B + 0.5B cos[2πfn]],

where A is the strength of the flange, B is the longest delay (measured in samples), and the frequency f (measured in cycles/sample) refers to the speed of the delay change. Complete the following:

i.   Using the flange strength A1, the longest delay B1, the flange frequency f1 (in cycles/sample), and the time-domain  difference  equation  in a for-loop, pass your original audio signal Q1.audioRaw (not the noisy audio or isolated noise) through the flanger. Ensure that the output has the same length as the input.     Assign the flanging output to Q1.audioFlange.

Hint: The index variable must be a positive integer.

Hint: Assign the output a value of 0 for values of n where x[n − 0.5B + 0.5B cos[2πfn]] is outside the indexable range of x[n].

ii.  Briefly (in no more than 2 lines of text) comment in u_lab.docx on how the output sounds.

2. (30 Marks) This question concerns interference and aliasing.

You are an engineer at SpaceZ and are receiving signals from the new deep space satellite deployed by SpaceY. You are tuning your terrestrial hardware using transmissions from the  satellite  and  have  collected  a  sequence  of  time-series  data  that  was  sampled  at frequency    f2s.    The    collected    data    is    in    the    vector    y2    in    your    signals    file u_lab_signals.mat. You are expecting to observe a periodic signal from the satellite with frequency components up to frequency fb. Please complete the following:

(a)  (9  marks)  Design  an  FIR  low  pass  digital  filter  for  the  satellite  signal  with  the windowing method. Complete the following:

i.     Using the window information tables in the lecture slides or notes, determine the shortest window type and length that will give a pass band ripple parameter below rp dB at frequencies less than fb, and that has a stop band defined by frequencies above fstop2. Remember that the sampling rate being used is f2s. Assign       window        type        as        a case-sensitive        character        array (either  ’rectwin’,  ’hann’,  ’hamming’,  or  ’blackman’)  to  Q2.w.  Assign  window length L to Q2.L. Note: You can assume that the tables are accurate.

ii.   Use the fir1 function and the corresponding window function to determine the unscaled impulse response h[n]. Use a cutoff frequency that is exactly halfway between fb and fstop2. Assign FIR impulse response vector h[n] to Q2.h.

iii.  Use your FIR low pass digital filter with the filter function (and not any function variant). Assign the low pass filter output to Q2.yLow.

(b)  (12 marks) Determine the spectra associated with Q2.yLow as follows:

i.     Calculate  the  double-sided  fast  Fourier  transform  (FFT)  of  Q2.yLow.  Do  not apply scaling. Assign the FFT output to vector Q2.FFT.

ii.    Each element in the FFT is associated with a frequency. Create the vector of frequencies  associated  with   Q2.FFT.  Assign  the  vector   of  frequencies  to Q2.fRange.

iii.  Plot the magnitude of Q2.FFT as a function of Hz frequency (i.e., a domain of [0,f2s)Hz   should   be    visible).   For    all   periodic    components    with   actual frequencies  up  to  fb,  label all corresponding  spectral  peaks  with  the  true component frequencies. You should assume that there is no aliasing. Save the FFT magnitude plot as a png file and include it in u_lab.docx.

(c)   (9 marks; “First Class Problem”) Suppose that one of the spectral peaks identified in Question 2(b) could bean alias (i.e., ignore the fact that Q2.yLow is the output of a lowpass filter). Complete the following:

i.    Calculate the lowest frequency signal (in Hz and rounded to the nearest Hz) that could lead to one of the spectral peaks as an alias. Briefly (in no more than 3 lines of text) explain your approach in u_lab.docx. Assign this frequency (in Hz) to Q2.fAlias.

ii.  Create a signal with frequency Q2.fAlias and plot its FFT to demonstrate that it would result in the alias as predicted. Label all corresponding spectral peaks.

Save the FFT magnitude plot as a png file and include it in u_lab.docx.

3. (20 Marks) This question concerns estimation of an unknown signal.

You area control engineering consultant and are visiting the factory of NewWave Mobile to   inspect   a   heating   chamber   that   will   be   used   to   stress-test   their   new   drone communication chips. Based on the chamber specification, you expect that the transient heating profile will behave according to the general equation provided in u_lab.txt where y3(t) is the temperature in degrees Celsius and w3(t) is the noise signal at time tin seconds.

You have collected noisy thermometer readings in column vector y3 in your signals file u_lab_signals.mat. Your data were collected starting from time t = 0 at the constant interval Ts3 in your parameter file. Please complete the following:

(a)  (3 marks) Construct the linear model observation matrix Θ needed to estimate the unknown parameters A3, B3, and C3 (in that respective order). Assign Θ to Q3.Obs.

(b)  (2 marks) Apply linear model estimation to estimate the unknown parameters A3, B3, and C3. Assign these three constants in the same order to the 3 × 1 column vector Q3.param.

(c)   (1 mark) Use the parameter estimates to predict the temperature for the same times at which the sensor values were taken. Assign the predicted temperatures to column vector Q3.yHat.

(d)  (1 mark) Calculate the mean square error of the predicted temperatures. Assign the scalar mean square error to Q3.mse.

(e)  (13 marks) Compare the spectra of the temperature sensor readings with those of the estimated temperatures, as follows:

i.     Calculate the double-sided fast Fourier transform  (FFT) of y3. Assign the FFT output to vector Q3.yFFT.

ii.    Each element in the FFT is associated with a frequency. Create the vector of frequencies  associated  with   Q3.FFT.  Assign  the  vector   of  frequencies  to Q3.fRange.

iii.  Calculate the fast Fourier transform (FFT) of Q3.yHat. Assign the FFT output to vector Q3.yHatFFT.

iv.  Plot the magnitude of both FFT outputs as a function of Hz frequency (i.e., a domain of [0,1/Ts3)Hz should be visible). Include both sets of spectra on the same axes. Label all relevant spectral peaks. Save the FFT magnitude plot as a png file and include it in u_lab.docx.

v.    In no more than 5 lines of text, comment in u_lab.docx on the accuracy of

the model. Would a time-domain plot be helpful to verify the accuracy?

4. (20 Marks) This question concerns the estimation of FIR filter coefficients.

You work for NewWave 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  determined that there are four primary signal paths of interest: the direct path from the base station and three paths that reflect off of the clouds. The reflections arrive later than the direct signal, such that the total received signal voltage y4[n]  is the  output  of a  noisy  difference  equation  of the  form provided in u_lab.txt, where w4[n] is the noise signal.

You have collected samples of the received signal voltage (in Volts) y4[n] based on the transmission of a pseudo-random pilot sequence x4[n]. These are given as the column

vectors y4 and x4, respectively, in your signals file u_lab_signals.mat. Please answer the following:

(a)  (4 marks) Construct the linear model 4-column observation matrix Θ needed to estimate the unknown FIR filter coefficients A4, B4, C4, and D4 (in that respective order). Assign the 4-column Θ matrix to Q4.Obs.

(b)  (6  marks)  There  was  a  sensor  malfunction  in  your  recording  equipment  while measuring y4[n], such that the variance of w4[n] gradually increased by a constant multiplicative  factor  of  k4  for  each  of  the  last  s4  samples   (as   described  in u_lab.txt). This means that the first sample after the malfunction had a noise variance  k4  times  greater  than  the  samples  before  the  malfunction,  the  second sample after the malfunction had a noise variance k42 times greater than the samples before the malfunction, and so on. Determine an appropriate weight column vector W [n] that can be used to perform weighted least squares estimation using the entire data set. Assign W [n] to Q4.W.

(c)   (2 marks) Apply linear model estimation (using weighted least squares) to estimate the FIR filter coefficients A4, B4, C4, and D4. Assign these four constants in the same order to the 4 × 1 column vector Q4.param.

(d)  (1 mark) Use the FIR filter coefficient estimates to predict the voltage for the same pilot input sequence x4[n]. Assign the predicted voltages to column vector Q4.yHat.

(e)  (3 marks) Compare the measured voltages and predicted values in the time domain on the same axes in a single time-domain plot, where the x-axis is the sequence index and  the  y-axis  is  the  voltage.  Save  the  plot  as  a  png  file  and  include  it  in u_lab.docx.

(f)   (4 marks; “First Class Problem”) Suppose that the specified multiplicative factor k4 was measured incorrectly. Assuming that predicted voltage signal  Q4.yHat  is the correct noiseless signal, consider estimating the correct value of k4. In no more than 4 lines of text, propose an approach in u_lab.docx. You do not need to write any code.

4     Submission of Deliverables

Place your files into a folder named u_lab (where  is your student number). Zip the folder and call it u_lab.zip. The folder should contain:

1.  u_lab.m (where is your student number), containing your code.

2.  u_lab_signals.mat  (where    is your student number),  containing your assigned signals. This file should be unchanged from the version that you downloaded.

3.  u_lab_Audio.mat (where is your student number), containing your original audio recording.

4.  u_lab_Answers.mat  (where    is your  student  number),  containing  the answers generated by your code.