# Prelab 4 - Autocorrelation

### Summary

In this prelab, you get familiarized with two common tasks in speech signal analysis: voicing determination and autocorrelation.

## Part 1 - Voiced/Unvoiced Detector

Voiced/unvoiced signal classification is an incredibly well-studied field with a number of vetted solutions such as Rabiner's pattern recognition approach or Bachu's zero-crossing rate approach. Pitch shifting (next lab) does not require highly-accurate voiced/unvoiced detection however, so we will use a much simpler technique.

The energy of a signal can be a useful surrogate for voiced/unvoiced classification. Put simply, if a signal has enough energy, we assume it is voiced and continue our pitch analysis. The energy of a discrete-time signal is given as follows:

Assignment 1

Using the given test speech signal and the test code given below, determine a useful threshold for $E_s$ and classify frames as voiced (return 1) or unvoiced (return 0). The test code will plot the results for you.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 import numpy as np import matplotlib.pyplot as plt from scipy.io.wavfile import read, write FRAME_SIZE = 2048 def ece420ProcessFrame(frame): isVoiced = 0 #### YOUR CODE HERE #### return isVoiced ################# GIVEN CODE BELOW ##################### Fs, data = read('test_vector.wav') numFrames = int(len(data) / FRAME_SIZE) framesVoiced = np.zeros(numFrames) for i in range(numFrames): frame = data[i * FRAME_SIZE : (i + 1) * FRAME_SIZE] framesVoiced[i] = ece420ProcessFrame(frame.astype(float)) plt.figure() plt.stem(framesVoiced) plt.show() 

## Part 2 - Autocorrelation

Autocorrelation is the process of circularly convolving a signal with itself. That is, for a real signal, the discrete autocorrelation is given as:

where $\tilde{x}[-n]$ is the complex conjugate of the time reversal of $x[n]$. The output $R_{xx}[l]$ measures how self-similar a signal is if shifted by some lag $l$. If normalized to 1 at zero lag, this can be written equivalently as:

For a periodic signal, the lag $l$ that maximizes $R_{xx}[l]$ indicates the frequency of the signal. In other words, the signal takes $l$ samples before repeating itself. This algorithm, combined with some additional modifications to prevent harmonics from being detected, comprises the most well-known frequency estimator for speech and music.

Assignment 2

Calculate and plot the autocorrelation of the test signal tune using the test code below. You may not use np.correlate() or other such functions.

Question

Indicate the value of lag $l$ that maximizes $R_{xx}[l]$. What is the signal frequency that corresponds to this lag?

### Python test code

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 import numpy as np import matplotlib.pyplot as plt fs = 8000 # Sampling Rate is 8000 duration = 1 # 1 sec t = np.linspace(0,duration,duration*fs) freq = 10 # Tune Frequency is 10 Hz tune = np.sin(2*np.pi*freq*t) # Add some Gaussian noise tune += np.random.normal(0, 0.5, duration * fs) plt.figure() plt.plot() # Start a new figure for your autocorrelation plot plt.figure() # Your code here # Only call plt.show() at the very end of the script plt.show()