Description

EE 242 Lab 1 – Modifying Signals

In this lab, you will work through a series of exercises to introduce you to working with audio signals and explore the impact of different amplitude and time operations on signals. This is a two-week lab. You should plan on completing the first 2 assignments in the first week.

Lab 1 Turn-in Checklist
• Pre-lab (upload to canvas before lab)
• Lab 1 Jupyter notebook with code for the first 4 exercises assignment in separate cells. Each assignment cell should contain markdown cells (same as lab overview cells) for the responses to lab report questions. Include your lab members’ names at the top of the notebook.
• 1 individual Jupyter notebook with code + markdown cells for the last exercise

Note: The pre-lab should be done individually, and all other assignments should be completed in groups of 3-4 people.

Pre-lab
Read the Lab 1 Background document, then complete the following exercises.
1. An audio signal y(t) is sampled with fs=32 kHz. What sampling period does that correspond to? If you mistakenly play the signal with fs=16 kHz, will it be shorter or longer than the original? How else will it sound different?
2. The envelope of an audio signal y(t) (the train sound that you will work with in this lab) is approximated below:

a. Sketch the signal y(2t). Label the height and the time points corresponding to t = 0, t = 0.5, t = 1.6 after the time scaling. If you played y(2t), would it sound like y(t) has higher frequencies or lower frequencies?
b. Repeat (a) for the signal y(0.5t)
c. Sketch the signal y(t-1) and y(t+0.5), again labeling critical time points.
3. When the signal is digitized, you need to implement the time shift in terms of the number of samples: y[n-n1] and y[n+n2]. Find n1 and n2 (corresponding to t1=1 and t2=0.5, respectively) for the case when fs=32kHz.
Download Lab 1 template (TemplateL1.ipynb) and rename it Lab1-XYZ, where XYZ are the initials of the lab partners. Your Lab 1 notebook should be organized according to this template.
Team Lab Assignments
This lab has 4 exercises to be completed as a team. Each should be given a separate code cell in your Notebook, followed by a markdown cell with report discussion. Your notebook should start with a markdown title and overview cell, which should be followed by an import cell that has the import statements for all assignments. For this assignment, you will need to import: numpy, the wavfile package from scipy.io, simpleaudio, and matplotlib.pyplot.
Assignment 1: Working with Sound Files
Start a new cell following the guidelines in the Lab 1 template, dividing it into Parts A-C.
A. Download the train.wav sound file provided. Using the scipy.io wavfile package (see Background document), read in the file using the saving the audio vector and sampling frequency in variables x1 and fs1, respectively. Print the sampling rate (which should be 32kHz) and the shape of x1, which will tell you the length and number of channels.
B. Write out two new versions of the file in wav format using different sampling rates: fs2=fs1/2 (16 kHz) and fs3=1.5*fs1. Note that the wav.write function requires the sampling frequency to be an integer. Also, the simpleaudio package is limited in the sa.mpling frequencies that it will support, so you cannot use arbitrary frequencies.
C. Using the simpleaudio package (see Background document), read in the three different versions of the train sound file and play each one.
Report discussion: Comment on how the audio changes when the incorrect sampling frequency is used.

Assignment 2: Amplitude Operations on Signals
Again, following the guidelines in the Lab 1 template, start a new cell and write a script to meet the following specifications. This assignment will have four parts, A-C, each of which should be indicated with comments.
A. Create a discrete time signal s1 that is the same length as x1 and has value 1 for t=[0,0.5] and value 0.2 for t>0.5. You can use the command below where len1 is the length of x1 and n0 is the index corresponding to t=0.5 s1 = np.concatenate((np.ones(n0),0.2*np.ones(len(x1)-n0))
Multiply x1 with s1 to create v1. Save this signal to a wav file.
B. Create a discrete-time decaying ramp signal r1, that is the same length as x1. The signal should have value 1 at time 0 and linearly decay to value 0. (Hint: use numpy.arange.) Multiply x1 with r1 to create v2. Save this signal to a wav file.
C. Read in v1 and v2 using simpleaudio and play the two different modifications together with the original, to verify that the volume of the second whistle is reduced.

Report discussion: Discuss the differences that the two modifications have on the signal. What would happen if you defined s1 to take value 2 for the [0,0.5] range? If you wanted a smooth but faster decay in amplitude, what signal might you use?

Assignment 3: Time Scaling Audio Signals
This assignment will have four parts, A-D, each of which should be indicated with comments.
A. Replicate the timescale function in the Lab 1 background document, and save it in its own cell, as indicated in the Lab 1 template.
B. Use the timescale function to obtain w(t)=x1(2t) and v(t)=x1(0.5t)
a. Create w(t) using a=2 and store the outputs of the timescale function as w and t_w.
b. Create v(t) using a=0.5 and store the outputs of the timescale function as v and t_v.
c. Create a time-reversed version of the signal z(t)=x1(-t) by reversing the order of elements in the sequence. In order to plot in parallel with other signals, use the time vector t_z = t_x1.
Note: When trying to play z(t), you might get a C-contiguous error. To fix this, use z(t) = np.ascontiguousarray(z(t)).
d. Save the resulting signal to a wav file.
C. Load a figure and plot the four signals (x1, w, v, and z) using a 4×1 subplot. Adjust the x and y axis limits to have the same ranges in both plots. Be sure to title the plots and label axes appropriately. For the time axis, you should plot time in msec, for which you will need to multiple the time array by 1000 as in the example in the Background document. Do not use grids on the subplots. Adjust the spacing to avoid overlap. If you have implemented the code correctly, the figure should look something like this.

D. Read in the signals you created using simpleaudio and play them to verify that they sound different based on what you would expect from these transformations.
Report discussion: Suppose a student runs the figure command before every call to subplot. When you run your script, what changes do you expect to see? How will the plots change?

Assignment 4: Time Shift Operation
We will now implement and test a timeshift function. This assignment will have four parts, A-D, each of which should be indicated with comments, following the guidelines in the Lab 1 template.
A. Write a function called timeshift that takes as input: a signal x, the sampling frequency fs (in Hz), and a time shift t0 (in seconds). The function should implement y(t) = x(t+t0) and produce as output the portion of the shifted signal starting at time 0. Assume that the original signal has value zero outside the time window. Your function should:
1. Find the integer shift n0 given t0 and fs.
2. Use conditional control that tests whether the time shift is positive or negative
1. For a time delay, create y by concatenating a zero vector with the original signal. (The output should be longer than the original signal.)
2. For a time advance, create y by copying the portion of the starting from n0 and then appending n0 zeroes at the end of the signal. (The output should be the same length as the original signal.)
3. Based on the length of the final signal and the sampling frequency, create a time vector that corresponds to the output signal length, starting at 0.
4. Return the new signal and the time vector.
Save the function it in its own cell, as indicated in the Lab 1 template.
B. Use the function to create x1(t+0.5) and x1(t-2). Plot the shifted signals with the original in a 3×1 plot: x1(t), x1(t+0.5), and x1(t-2). The x-axis should be between 0 and 4 for all three plots. Label axes and title the plot.
C. Play all three signals. For the signal that has been advanced, you should be able to hear that part of the sound is missing, since we have not preserved those samples.
Report discussion: There is a trivial case that you should ideally test for. If the shift is zero, then the output is the original signal. If the shift is an advance bigger than the original signal, then the output will be zero. Comment on whether your current implementation correctly handles these cases and whether there is a better implementation.

Team Report

KEEP READING! There’s one more assignment that you do on your own.

Individual Assignment: Create Your Own Sound Mash-Up
Start a new notebook following the guidelines in the Lab 1 template. Download 1-2 new sounds, which could be from the extras provided, from some open repository or from your own collection. Keep them short. If you choose a sound that has 2 channels, extract audio data from only one channel.