find_delay documentation
What is find_delay?
find_delay is a Python package that tries to find the delay where a time series appear in another via cross-correlation. It can theoretically work with any time series, but was created to try to align audio files.
How do I install find_delay?
You can install find_delay using:
python3 -m pip install find-delay
py -m pip install find-delay
Once it is installed, you can import find_delay into your script via:
import find_delay
You can then use find_delay.find_delay() or find_delay.find_delays().
Important
The proper name of the package is find_delay
, with an underscore. Use it when importing the package in any of
your projects. However, PIP (the Package Installer for Python) automatically converts underscores to dashes when
creating packages, to uniformize with other programming languages. Hence, when installing the package in an
environment, you should run `pip install find-delay`
(with a dash). Note that calling
`pip install find_delay`
(with an underscore) should also work most of the time.
How do I use find_delay?
To find when an excerpt starts in an array, use the find_delay function and fill only the first five parameters:
array_1
: An array of numbers or the path to a WAV file
array_2
: An excerpt of array_1, or the path to a WAV file contained in array_1
freq_array_1
: The frequency of the array (if it’s important, otherwise set it at 1). If array_1 is a path to a WAV file, you can ignore this parameter.
freq_array_2
: The frequency of the excerpt (it it’s important, otherwise set it at 1). If array_2 is a path to a WAV file, you can ignore this parameter.
compute_envelope
: If you are trying to find the delay between two audio files, set on True, otherwise False.
Leave the other parameters default (just set plot_figure = True
if you want to visualize the output of the
function). This should be enough for most cases, but you can fine tune other parameters of which you can find the
description here.
If you need to find multiple excerpts into one big array, call find_delays instead.
Examples
Example 1: two arrays of random numbers
array_1 = [24, 70, 28, 59, 13, 97, 63, 30, 89, 4, 8, 15, 16, 23, 42, 37, 70, 18, 59, 48, 41, 83, 99, 6, 24, 86]
array_2 = [4, 8, 15, 16, 23, 42]
find_delay(array_1, array_2, 1, 1, False, path_figure="figure_1.png")

Example 2: sine function, different frequencies
timestamps_1 = np.linspace(0, np.pi * 2, 200001)
array_1 = np.sin(timestamps_1)
timestamps_2 = np.linspace(np.pi * 0.5, np.pi * 0.75, 6001)
array_2 = np.sin(timestamps_2)
find_delay(array_1, array_2, 100000 / np.pi, 6000 / (np.pi / 4),
compute_envelope=False, resampling_rate=1000, window_size_res=20000, overlap_ratio_res=0.5,
resampling_mode="cubic", plot_figure=True, path_figure="figure_2.png",
plot_intermediate_steps=True, verbosity=1)

Example 3: audio files, different frequencies
audio_path = "i_have_a_dream_full_speech.wav"
audio_wav = wavfile.read(audio_path)
audio_frequency = audio_wav[0]
audio_array = audio_wav[1][:, 0] # Turn to mono
excerpt_path = "i_have_a_dream_excerpt.wav"
excerpt_wav = wavfile.read(excerpt_path)
excerpt_frequency = excerpt_wav[0]
excerpt_array = excerpt_wav[1][:, 0] # Turn to mono
find_delay(audio_array, excerpt_array, audio_frequency, excerpt_frequency,
compute_envelope=True, window_size_env=1e6, overlap_ratio_env=0.5,
resampling_rate=1000, window_size_res=1e7, overlap_ratio_res=0.5, return_delay_format="timedelta",
resampling_mode="cubic", plot_figure=True, path_figure="figure_3.png",
plot_intermediate_steps=True, verbosity=1)

How does it work?
The function accepts two arrays containing time series - the time series can be of different frequency or amplitude. To obtain better results, make sure that the second time series (the excerpt) is entirely contained into the first - notably, you can trim the second array for it to be the case. The function should work if the second array is over one of the edges of the first, but the cross-correlation score will never be 1. This implies that, the less amount of the second array contained in the second, the more likely the chance of getting an erroneous result.
The function can calculate the envelope of the time series (recommended for audio files) and apply a band-pass filter to the result.
The function can also resample the arrays (necessary when the two time series do not have the same frequency).
Finally, the function performs the cross-correlation between the two arrays.
The results can be then plotted if the corresponding parameters are activated, and the function returns the delay at which to find the second array in the first by selecting the delay with the maximum correlation value (optionally, the function can also return this correlation value).