Finding a best-describing underlying beat in a sequence can be done using Fourier transforms, where we decompose a signal into its frequency components.
%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:
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.
from thebeat.stats import fft_plot
fft_plot(seq, unit_size=1000);
On the x axis we see the number of 'cycles per second'. We chose a unit size of 1000 (ms), and so 100 cycles per unit in our case means 100 cycles per second. That's very fast, and we probably don't expect some sort of underlying beat to happen at that pace. So, we limit the x axis by setting x_max to 10 (i.e. 10 Hz, or a beat IOI of 100 ms, in our case).
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.
from thebeat.stats import fft_values
# Get x and y data
x, y = fft_values(seq, unit_size=1000, x_max=10)
# Subset data so that we skip the max power at x = 0
x, y = x[1:], y[1:]
# Get index of maximum y value
max_y_index = np.argmax(y)
max_x = x[max_y_index]
print(f"The largest peak is at {max_x} Hz")
print(f"This corresponds to a beat IOI of {1000 / max_x} ms")