Beat-finding using Fourier transform¶

Finding a best-describing underlying beat in a sequence can be done using Fourier transforms, where we decompose a signal into its frequency components.

In [2]:

%matplotlib inline
import warnings
warnings.filterwarnings('ignore', message="Matplotlib ")

We create an example sequence, and initiate a random number generator with a seed, so you will get the same output as we:

In [3]:

from thebeat import Sequence
import numpy as np

rng = np.random.default_rng(seed=123)

seq = Sequence.generate_random_normal(n_events=100, mu=500, sigma=25, rng=rng)

Now we plot the Fourier transform. Because we created our Sequence object using millisecond values, we will choose a unit size of 1000.

In [4]:

from thebeat.stats import fft_plot

fft_plot(seq, unit_size=1000);

To investigate the plot in more detail, we can limit the x axis, which will help:

In [5]:

fft_plot(seq, unit_size=1000, x_max=10);

We see a very clear peak at around 2 cycles per second, i.e. every 500 ms.

In [6]:

# Create the plot
fig, ax = fft_plot(seq, unit_size=1000, x_max=10)

# Get the data
x_data, y_data = ax.lines[0].get_data()

# Get the index of the highest value for y, and get its corresponding x value
max_y_index = np.argmax(y_data)
max_x = x_data[max_y_index]
print(1000 / max_x)

501.8585858585858