Lab 3

MAE 170 [FA23]: LAB 3 Acquiring Signals: A/D Conversion, Sampling, and Aliasing Submit your answers to the questions posed in this lab to gradescope and turnitin via the Canvas course website by 11:59 pm (midnight) the evening before your next lab section. Learning objectives ● LLO2-1: Learn how to determine the resolution of a signal processing device. ● LLO2-2: Understand the importance of sampling rate, and be able to predict onset of aliasing and aliased frequencies. ● LLO2-3: Understand and be able to apply signal conditioning techniques, such as analog filtering. ● LLO2-4: Understand the origin of, and be able to identify, signal processing artifacts (e.g. from aliasing) ● LLO2-5: Be able to interpret frequency domain information and apply Fast Fourier transforms (amplitude, shape of typical signals, resolution in frequency domain, sampling rate) ● LLO2-6: Be able to acquire analog signals with an arduino and/or an oscilloscope and download the information in an automatable fashion (including, where helpful, real-time analysis). ● LLO2-7: Gain experience with communicating observations and their experimental context via technical writing ● LLO2-8: Gain experience with presenting information visually in a manner that is accessible and information dense. ● LLO2-9: Gain experience with norms and ethics in data analysis and presentation.

MAE 170 [FA23]: LAB 3 PRE-LAB: Practice visualizing the effect of aliasing, via the time and frequency domain. To actively see what happens to a discretely sampled single, fixed frequency (~125 Hz) signal as you change the sampling frequency, use Aliasing.mlapp , which is found on canvas under files→Lab 2→Matlab files . View the Arduino Lecture 2 video . View the following Matlab tutorial videos: ● Using Basic Plotting Functions ● Processing an Excel file in MATLAB ○ Note: dlmread works in an analogous manner for text files, with varied data delimiters Read the following via the custom course textbook: ● Part B (Ohm’s and Kirchoff’s laws, parallel and series circuits) ● Part A.1-3, 7, 8, 13, 14, 15 Review the appendix for this set of lab instructions. We expect that you have read, in detail, the lab instructions before coming to the lab. Much of Part I can be tested, and a portion of Part III completed, before coming into the lab (and it is highly recommended you do so). 2

MAE 170 [FA23]: LAB 3 increase the measurement range on your DMM (or vice versa, if your measured signal is too small to achieve satisfactory precision). Be sure to note the units on your DMM display. Upload the following script to the Arduino, which reads the voltage on analog input channel A0, and writes the information to the serial output stream in the format: “data on serial stream in counts, time in microseconds”. Key note: This process is an analog to digital conversion (A/D). Example code: // Arduino serial read script // the setup routine runs once when you press reset: void setup() { // initialize serial communication at 115200 bits per second: Serial.begin(115200); } // the loop routine runs over and over again forever // the loop contains reading the analog in A0 pin and writing the voltage to the serial port // followed by the time in microseconds: void loop() { Serial.print(analogRead(A0)); Serial.print(", "); Serial.println(micros()); } Open the serial monitor under the tools drop down menu in the Arduino IDE. Turn the knob on the potentiometer from left to right and observe how the data in the first column changes. Q1: Is the variable voltage applied to channel A0 an analog or digital signal? Q2: What are the minimum and maximum values in the serial stream (first column, in “counts”, where counts are the Arduino input channel A/D measurement intervals)? What voltages do these minimum/maximum counts correspond to on your DMM? Q3: Given the information in Q2, approximately what is the resolution of your Arduino input channel A0 A/D converter (in volts)? As described in lecture, we can define the resolution via the following equation: 4

MAE 170 [FA23]: LAB 3 , (1) ∆𝑋 = |𝑋 ?𝑎𝑥 −𝑋 ?𝑖? | 2 ? where in Eq. (1), is your resolution (in this case, in units of Volts), is the lower ∆𝑋 𝑋 ?𝑖? value of your range, is the upper value of your range, and is the number of bits. 𝑋 ?𝑎𝑥 ? Q4: What does the denominator in Eq. (1) represent? The Arduino analog input channels on default settings have a range of 0 to 5 V, which corresponds to counts, or of 0 to 1023. Q5: What is the number of bits of the Arduino analog input channel A0 A/D converter? Q6: What is the resolution (in volts) of the Arduino analog input channel A0 A/D converter, based on Eq. (1)? How does this compare to what you found in Q4? Discuss any differences and speculate as to potential causes. We are now going to use Matlab on your computer to read the serial stream (in this case being constantly sent by the Arduino, via the script you uploaded, with information about the voltage on the A0 pin), instead of the Arduino IDE serial monitor. In the future this will allow more complex functionalities and analysis of your experimental data. In the following, you are going to build a Matlab script, using the code snippets below, that reads the data from the serial port for some specified sampling time, at some specified sampling rate, and generates a figure with that data. This process repeats until a key (other than “P”) is pressed, whereafter it saves the measured data into a figure file, a comma separated value (CSV) file, and a mat file, all of which show the same time vs. voltage data, but give you a variety of ways to access your data. The three files will be saved to your current active Matlab directory, which is the same as the folder where the code you are running is located. For any uncertainties in the Matlab script syntax, you can copy each command into a google search. Matlab maintains a highly comprehensive description of every function online. You can also use the “help” function in the Matlab command line ( https://www.mathworks.com/help/matlab/ref/help.html ). Clear variables, windows, and reset instrument interface objects. close all ; %close all open windows clear all ; %clear all variables clc; %clear output screen instrreset; % reset interface objects 5

MAE 170 [FA23]: LAB 3 flush(s); end Create another loop inside the main one, read data from the serial stream for your specified sampling time at a rate as close to your specified sampling rate as possible. while flag==0 out=char(readline(s)); % reading the serial port ind=find(out== ',' ,1); a=str2double(out(1:ind-1)); t=str2double(out(ind+2:end))/1E6; if (t-timer)>dt_set % condition to take sample at set sampling rate time(i) = t; % establishing time steps for sampling frequency A(i)=a; timer=time(i); i=i+1; if t>(T+time(1)) % condition to end loop when end time is reached flag=1; end end end Close your serial object. disp( 'Done! Be sure to zoom in to see the finite Arduino resolution.' ) clear s; % closes serial port Make the time vector start at 0, convert the counts to voltage, and calculate the actual, average sampling frequency attained by the Arduino. reps=i-1; time = time(1:reps)-time(1); % setup a vector for time voltage = 5/1023*A(1:reps); % convert serial amplitude to voltage dt_avg = time(end)/reps; % find the average time interval between samples fs_avg=1/dt_avg; % calculate the average sampling frequency from dt_avg Plot your data. Note the automated, time saving method for creating well formatted figures. %% Create plot figure(01); % setup figure 01 % plot time vs. voltage, set plotting style to line and dots of size 8 plot(time, voltage(1:reps), '-o' , 'LineWidth' ,2, 'MarkerSize' ,4); xlabel( 'time (s)' ); % x-axis label name ylabel( 'voltage (V)' ); % y-axis label name ylim([min(voltage)-abs(0.1*max(voltage)) ... 7

MAE 170 [FA23]: LAB 3 max(voltage)+abs(0.1*max(voltage))]); % set y plot range title([ 'Voltage vs. Time Sample' ]); % set title % get current plot axes, set font and line width set(gca, 'FontSize' ,22, 'LineWidth' ,2); set(gcf, 'units' , 'normalized' ); % set plot sizing to normalized units drawnow % draw the figure now Save your data. save( 'MAE170_lab2part1' , 'time' , 'voltage' ); % save time and voltage to mat file csvwrite( 'MAE170_lab2part1' , [time, voltage] ); % save time and voltage to csv file saveas(gcf, 'MAE170_lab2part1' ); % save figure Slowly turn the knob on your potentiometer while the code is running, and observe the changing voltage in the generated figure. Q7: Resave the figure file that you generated (zooming in until you can show the discrete steps induced by finite, digital resolution) as a .jpg image, and upload it with your lab assignment submission, as an answer to this question. 8

MAE 170 [FA23]: LAB 3 connected to the GND and A0 ports on the Arduino. Make sure to turn the output of the function generator on by pressing the ‘Channel’ key and choosing from the menu on the screen, and that it is set to “High Z” mode. As for the prior part, you will construct a Matlab script to not only read your Arduino, but also to read the oscilloscope data! This first portion should be familiar from the last Part’s Matlab script, and is intended to read the serial stream from the Arduino, but now only once per each time the script is run, for a sample time of one second. close all ; %close all open windows clear all ; %clear all variables clc; %clear output screen instrreset; % reset interface objects %% Parameters to set sampleT=1; %Set sampling time in seconds % create the serial object 'dataLogger' % you must replace the port name with the port on your machine % you can find this through the arduino interface (tools->port) % the baud rate must match what you selected in your serial read ... % Ardino code dataLogger=serialport( 'COM4' ,115200); %Connect to arduino %% Arduino data capture newV=0; %intialize variables newT=0; %intialize variables tempText=readline(dataLogger); startV = str2double(extractBefore(tempText, ',' )); startT = str2double(strtrim(extractAfter(tempText, ',' ))); vArduino = [startV*5.0/1023]; tArduino = [0]; while newT<sampleT tempText=readline(dataLogger); newV=str2double(extractBefore(tempText, ',' ))*5.0/1023; newT=(str2double(strtrim(extractAfter(tempText, ',' )))-startT)/1E6; vArduino = [vArduino newV]; tArduino = [tArduino newT]; end clear dataLogger ; %delete dataLogger variable so you can use the com port again Now we will set up the process to read data from the oscilloscope. We are going to make a separate function called “oscread”, and call that function. The function call is the following line. %% Read oscilloscope data 10

MAE 170 [FA23]: LAB 3 [vOscope,tOscope]=oscread(); Now write the function. function [wave,time] = oscread() Set the buffer size (how much data it can acquire at one time) and set up the oscilloscope communication object (see the VISA protocol https://www.mathworks.com/help/instrument/visa-interface.html , as well as the Programming guide for our Rigol Oscilloscopes: https://www.batronix.com/pdf/Rigol/ProgrammingGuide/DS1000DE_ProgrammingGuide _EN.pdf ). The oscilloscope device ID (highlighted in teal) must be adjusted to match the ID printed on the front/back of the particular oscilloscope (also can be found under utility → system info on the oscilloscope). %% may need to use tmtool to scan for oscilloscope resource buffer=2048; % buffer size % set oscilloscope visa object oscObj = visa( 'NI' , 'USB0::0x1AB1::0x0588::DS1ET213707925::0' ); oscObj.InputBufferSize = buffer; % Set the buffer size Open the oscilloscope connection object. fopen(oscObj) % Open oscilloscope connection Tell the oscilloscope to pull data from Channel 1 using text (fprint) commands. fprintf(oscObj, ':wav:data?' ); % Pull data from Channel 1 [data,len]=fread(oscObj,buffer); % Read data to matlab Ask the oscilloscope what scales it is set for (time and voltage). timebase=str2double(query(oscObj, ':TIMebase:SCALe?' )); %get timescale %get vertical scale and offset verticalscale=str2double(query(oscObj, ':CHANnel1:SCALe?' )) verticaloffset=str2double(query(oscObj, ':CHANnel1:OFFSet?' )) Use the acquired scales to correctly set the time and amplitude values. wave=(125-data(12:len-1)')*verticalscale/25-verticaloffset; % calibration determined by inspection T=timebase*12; % calculate total time dt=T/length(wave); % calculate time step 11

MAE 170 [FA23]: LAB 3 Plot your time-voltage signal. figure(1); plot(time, signal, '-ob' , 'LineWidth' ,2, 'MarkerSize' ,4); set(gca, 'FontSize' ,22, 'LineWidth' ,2); xlabel( 'time (s)' ) ylabel( 'Amplitude (a.u.)' ); Call a function you created to calculate the FFT of your data. [freq, amp]=MAE170fft(time, signal); Plot your FFT spectrum. figure(2) semilogy(freq, amp, '-ob' , 'LineWidth' ,2, 'MarkerSize' ,4); set(gca, 'FontSize' ,22, 'LineWidth' ,2); xlabel( 'frequency [Hz]' ) ylabel( '|FT|' ); Create your FFT calculation function. function [frequencyVar, amplitudeVar] = MAE170fft(tVar, yVar) reps=length(tVar); % obtain number of samples fs=1/mean(diff(tVar)); % calculate mean sampling rate % calculate oscilloscope signal PSD [PSD,f_psd] = periodogram(yVar, ... rectwin(reps),reps,fs, 'onesided' ); frequencyVar = f_psd; amplitudeVar = sqrt(PSD); end Q8: (a) Identify the frequency with the largest amplitude, greater than 10Hz, in each dataset by plotting the Fourier transforms of each dataset (these plots do not need to be turned in with your assignment). Plot these identified (most pronounced) frequencies vs. the input frequencies, using Matlab, in the form of discrete markers (this plot should be turned in with your assignment). (b) On the same plot, also plot two lines a piecewise line showing the predicted alias frequencies, given by Eq. (1) in the Appendix. Draw a vertical dashed line at the frequency where you predict aliasing to start occurring for each the Arduino’s sampling frequency. 13

MAE 170 [FA23]: LAB 3 Q9: What happens to the measured or aliased frequency when the input frequency crosses the dashed line corresponding to that group of datasets? Describe your answer in 1 to 3 sentences. Q10: One way to detect if an observed signal or frequency component is aliased, is to change the sampling frequency and repeat the measurement. What would happen to the measured frequency, if you do this, and the sample is (or is not) aliased? Q11: (BONUS): When analyzing the data there is a large peak around 0 Hz, what is the reason for this? 14

MAE 170 [FA23]: LAB 3 Q13: This question pertains to WLO2: Be able to present data visually in an accessible and information dense manner. In Q9, you created a figure. Write a caption for this figure, and ensure both the figure and the caption satisfy the dimensions of WLO2 provided below. WLO2: Be able to present data visually in an accessible and information-dense manner [Figures and Tables]. Organization of information: − Effective consolidation of data; Appropriate amount of data displayed in one figure, such that figure is easily read and comparison between data sets can be easily conducted. − Every figure must be referred to in the text. Data accuracy: − Accuracy/precision of data evident. Figure formatting: − Axes: 1) Appropriate size to be readable; 2) Clearly labeled with units specified; 3) Well placed axes; 4) Convenient (for clarity) choice of scaling (log vs. linear) for chosen discussion points; Closely fitted range selection (fits data displayed); 5) x-independent variable / y-dependent variable. − Data markers and trendlines are easily readable. − Clear differentiation between discretely and continuously sampled data. − Theoretical vs. experimental vs. fitted trend lines clearly differentiated. − Sparsely vs. near-continuous sampling is differentiated. − Clear legend (if needed). − Caption (below figure) allows the reader to fully interpret the data shown in the figure. − Can be fully read in grayscale. − The caption serves as the figure’s title. A title above the figure is not used with a caption. Tables: − Clearly labeled rows and columns. − Descriptive title and caption (on top of table). − Appropriate amount of data, such that conclusions can be readily drawn by the reader. − Every table must be referred to in the text. 16

MAE 170 [FA23]: LAB 3 APPENDIX Aliasing in analog-to-digital conversion (SWR – 2013) If a signal sampled at frequency f s has frequency components >f s /2, after sampling those signals will be “aliased” or “folded back” into the DC - f s /2 range. The alias frequencies can be calculated as f alias = |f in - N·f s | (1) where N (0,1,2…) indicates the frequency band which contains the f in component in the original signal, and f alias is the shifted frequency of the f in signal after sampling. The frequency bands N are defined here as N Freq band 0 DC - f s /2 1 f s /2 - 3f s /2 2 3f s /2 - 5f s /2 3 5f s /2 - 7f s /2 4 7f s /2 – 9f s /2 5 and so on… Example: Assume a sampling frequency f s of 100 kHz and an analog data stream containing signal components at the following f in frequencies: 27 kHz, 41 kHz, 82 kHz, 219 kHz, and 294 kHz. After sampling, the amplitudes of all the signals would be preserved but their frequencies would be shifted or “folded” from f in to f alias according to Eq. (1) above: Table 1: f in vs f alias f s f in N f alias = | f in – N(f s ) | Description 100 kHz 27 kHz 0 | 27 – 0(100) = 27 kHz Correct signal, good data 100 kHz 41 kHz 0 |41 – 0(100)| = 41 kHz Correct signal, good data 100 kHz 82 kHz 1 |82 – 1(100)| = 18 kHz Aliased signal, data is artifact 100 kHz 219 kHz 2 |219 – 2(100)| = 19 kHz Aliased signal, data is artifact 100 kHz 294 kHz 3 |294 – 3(100)| = 6 kHz Aliased signal, data is artifact 17