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EEL 3135– Lab #02 solution

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EEL 3135– Lab #02
Submission Notes
• Your laboratory solutions should be submitted on Canvas as a single published MATLAB PDF.
• Use the provided skeleton code as the basis for your solutions (easier for you and the graders).
Question #1: (Audio Synthesizer) Download eel3135_lab02_comment.m from Canvas, replace each of the corresponding comments with the corresponding descriptions. This is designed
to show you how to work with audio in MATLAB.
Note: You should run the code to help you understand how it works and help you write your
comments. You will use elements of this MATLAB code for the rest of the lab assignment.
Question #2: Consider the three sinusoids below:

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Full Name:
EEL 3135– Lab #02
Submission Notes
• Your laboratory solutions should be submitted on Canvas as a single published MATLAB PDF.
• Use the provided skeleton code as the basis for your solutions (easier for you and the graders).
Question #1: (Audio Synthesizer) Download eel3135_lab02_comment.m from Canvas, replace each of the corresponding comments with the corresponding descriptions. This is designed
to show you how to work with audio in MATLAB.
Note: You should run the code to help you understand how it works and help you write your
comments. You will use elements of this MATLAB code for the rest of the lab assignment.
Question #2: Consider the three sinusoids below:
s1(t) = 3 cos ?
800πt −
π
3
?
s2(t) = 2 cos ?
800πt −
π
4
?
s3(t) = 2 cos ?
1200πt −
π
4
?
(a) Use the sampling frequency fs = 8000 Hz to generate the three sinusoids s1(t), s2(t), and
s3(t) over the time range from t = 0 to 0.01 second in MATLAB. Put the generated sinusoids
in MATLAB vectors s1, s2, and s3, respectively. Plot the three sinusoids in three separate
figures or subfigures. Label the axes of your figures appropriately. Use MATLAB’s axis
function to plot only the first four periods of the sinusoids.
(b) Use the MATLAB function audiowrite to generate a .wav file for each of the three sinusoids in (a). Note that you’ll need to rescale the values in your vectors to within the range
[−1, 1] before passing them as input to audiowrite by doing, say,
s1_scaled = s1/max(abs(s1));
and then pass s1 scaled to audiowrite as input. Remember to set also the sampling
frequency argument in audiowrite to the value of fs in (a). Save s1(t) to s1.wav, and so
on. Submit the .wav files together with your published report to Canvas. 1
(c) Let x1(t) = s1(t)+s2(t). Plot the first four periods of x1(t) and label the figure appropriately.
Use your hand-calculated expression of x1(t) to verify the plot. Check whether the amplitude,
phase, and frequency of the expression agrees with your theoretical expectation.
(d) Let x2(t) = s2(t)+s3(t). Plot the first four periods of x2(t) and label the figure appropriately.
Use your hand-calculated expression of x1(t) to verify the plot. Check whether the amplitude,
phase, and frequency of the expression agrees with your theoretical expectation.
1You can also use the MATLAB function soundsc to listen to the sinusoids without saving a file. Remember to
set the sampling frequency argument in soundsc. Note: if you use MATLAB through UF Apps or the ECE cluster,
you may not be able to hear any sound played by soundsc. In such case, play the .wav files generated in (b) to
listen to the sinusoids instead.
1
Question #3: This exercise expands the rudimentary music synthesizer in the comment code.
When you press and hold a key, a step sinusoid (more commonly refer to as a note) with a desired
frequency, phasor (amplitude and phase), and duration is played depending on the particular key
we press, how hard we press it, and for how long we hold it, respectively.
(a) Create a script that uses key_to_note and build_song(As, keys, durs) from the
previous question to play “Mary had a Little Lamb.” Let fs=8000; The A values, key
values, and dur values for the song can be stored in vectors:
As = [1 1 1 1 1 1 1 1 1 1 1 1 1];
keys = [44 42 40 42 44 44 44 42 42 42 44 47 47];
durs = [1 1 1 1 1 1 2 1 1 2 1 1 2]*1/4;
Run the script and get the sound checked off by your lab TA before moving on.
(b) Musical instruments generate signals with multiple sinusoids. Each sinusoid has varying
amplitudes and phases and the frequencies are integer multiples of a fundamental frequency
(just like a Fourier series). The harmonics determine the timbre (sound quality) of the note.
The following table contains the harmonics (integer multiples of frequency), amplitudes, and
phases to emulate a trumpet. Create a new function key_to_note_trumpet that creates
a trumpet sound.
k – Harmonic Ak – Amplitude φk – Relative Phase
1 0.1155 -2.1299
2 0.3417 +1.6727
3 0.1789 -2.5454
4 0.1232 +0.6607
5 0.0678 -2.0390
6 0.0473 +2.1597
7 0.0260 -1.0467
8 0.0045 +1.8581
9 0.0020 -2.3925
(c) Create a new version of build_song(As, keys, durs) and name this new function
build_song_trumpet(As, keys, durs). Use key_to_note_trumpet in the function and recreate the Mary song with trumpet notes. Make key now correspond to the
fundamental frequency. Get this sound checked off by your lab TA.
(d) Create a new song building function that accepts a different set of parameters:
build_song_time(As, keys, start_time, end_time). Replace dur input with
the following two inputs (both are in units of seconds):
start_time = [0 1 2 3 4 5 6 7 8 9 10 11 12]*1/4;
end_time = ([0 1 2 3 4 5 7 8 9 11 12 13 15]+0.2)*1/4;
Run the script and get the sound checked off by your lab TA. You can use the trumpet
or the original sound.
(e) Plot the output of build_song, build_song_trumpet,and build_song_time versus
time (in seconds) using the plot function. Be sure to properly label all axes (Amplitude
and Time), and title (using the title function) your plots to differentiate them.
(f) Answer: What are the key differences between the plots in (d)?
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