How to fit a sinusoidal graph to an audio signal in order to determine frequency and amplitude in Python?

Question

I have an audio signal which has a form similar to the below. I have tried to use Scipy's optimise library to fit a sine function to the data however this does not seem to work due to the form of the data. How else could I fit a sine function to determine the frequency and amplitude?

Answer 1

There are many ways to extract this information out of the data. You can (and probably should) apply some spectral analysis for the most accurate results. Check out SciPy's spectrogram , for instance. However, to quickly get an estimate of the frequency, you could just look at the zero-crossings:

import numpy as np
import matplotlib.pyplot as plt
from math import pi

# Generate a 2 second array of data with millisecond resolution
time, timestep = np.linspace(0, 2, 2000, endpoint=False, retstep=True)
# Generate a constant frequency sine wave with varying amplitude
frequency = 42
amplitude = 1 / ((time - 1)**2 + 0.03)
data = amplitude * np.sin(2*pi*frequency*time)
plt.plot(time, data)

# Extract rising zero crossings
rising_zero_crossing_indices = np.where(np.diff(np.sign(data)) > 0)[0]
rising_zero_crossing_times = time[rising_zero_crossing_indices]

# Find the frequency 
period = np.diff(rising_zero_crossing_times)
avg_frequency = 1/np.mean(period)

print(avg_frequency)