Prelab 5  Resampling
Summary
When Cher's song "Believe" hit shelves on October 22, 1998, music changed forever. Cher's single sold 11 million copies worldwide, earned her a Grammy Award, and topped the charts in 23 countries. AutoTune is the algorithm behind the success of "Believe". It was created by an ECE Illinois PhD alum, Dr. Andy Hildebrand. He came up with the idea of using autocorrelation to do pitch correction while working as an oil engineer at Exxon. We will explore a variant of AutoTune in more detail in the lab.
In this prelab, we will try a naive pitchshifting method: lowering the pitch by a factor of 3 and increasing the pitch by a factor of 2 using resampling.
Downloads
Submission Instruction
Refer to the Submission Instruction page for more information.
Part 1  Upsample by 3x
Upsampling a signal by a factor of 3 means inserting 2 zeros between each sample. For example, we insert zeros in this 20sample frame:
and get a 60sample signal:
Assignment 1
Load the given test audio and upsample by 3x. Plot the FFT of the original signal and the zeroinserted signal.
Note
The test audio is stereo, meaning it has two channels. You can conver it to monotone with data = data[:, 0]
.
Question
 What is the relationship between the original signal's FFT and the upsampled signal's FFT?
 How do we preserve the original information without introducing aliasing?
Part 2  Downsample by 2x
Downsampling a signal by a factor of 2 means removing every other sample. When played back at the same sampling rate, this results in a signal that sounds higherpitched
Assignment 2
Load the given test audio and downsample by 2x. Plot the FFT of the original signal and the downsampled signal.
Question
 What is the relationship between the original signal's FFT and the downsampled signal's FFT?
 How do we preserve the original information without introducing aliasing?
Part 3  Playback
Parts 1 and 2 (along with a couple other components) can be chained together to implement a resampler of any ratio . To get some intuition for the output of a resampled signal, we will use SciPy's resampling function scipy.signal.resample_poly. This can be called with the following code:
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from scipy import signal from scipy.io.wavfile import read from IPython.display import Audio Fs, data = read('test_audio.wav') data = data[:, 0] up_ratio = ?? down_ratio = ?? output = signal.resample_poly(data, up_ratio, down_ratio) Audio(output, rate=Fs) 
Assignment 3
Try a few resampling ratios, including at least .
Question
What does the resulting audio sound like? Be specific in your response. How do the vocal characteristics of the singer change?
Part 4  Preview
In lab 5, we will be implementing a cool autotune app using the method called TDPSOLA. Please watch this ~5 minutes video on doing TDPSOLA by hand which is very helpful for getting an intuitive understanding of TDPSOLA.
Grading
Prelab 5 will be graded as follows:

Assignment 1 [0.75 point]
Plots of FFT of the original and upsampled signal [0.5 point]
Short answer question [0.25 point]

Assignment 2 [0.75 point]
Plots of FFT of the original and downsampled signal [0.5 point]
Short answer question [0.25 point]

Assignment 3 [0.5 point]
Playback different resampling ratios [0.25 point]
Short answer question [0.25 point]