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librosa.util.interp_broadcast

librosa.util.interp_broadcast(*, x1, x1_pos, x2, x2_pos, interp_pos=None, op=<ufunc 'multiply'>, kind='linear', fill_value=0, axis=-2)[source]

Broadcast two arrays using interpolation

Interpolates two arrays along a given axis to a common grid, and performs a broadcast operation (eg. np.multiply) to combine them. It is useful for retrieving the DFT / AC product [1] and the Fundamental Tempogram [2].

[1]

Peeters, G. “Spectral and Temporal Periodicity Representations of Rhythm for the Automatic Classification of Music Audio Signal.” In IEEE Transactions on Audio, Speech, and Language Processing, vol. 19, no. 5, pp. 1242–1252, July 2011.

[2]

Cozens, James, and Simon Godsill. “Dynamic Time Signature Recognition, Tempo Inference, and Beat Tracking Through the Metrogram Transform.” In IEEE Open Journal of Signal Processing, pp. 1–9, 2023.

Parameters:
x1np.ndarray

An array with broadcast compatible dimensions (except along the axis of interpolation) with x2.

x1_posnp.ndarray

Positioning data along the axis of interpolation for x1.

x2np.ndarray

An array with broadcast compatible dimensions (except along the axis of interpolation) with x1.

x2_posnp.ndarray

Positioning data along the axis of interpolation for x2.

interp_posnp.ndarray

Positioning data for the interpolation grid. Default: x1_pos.

opfunction [optional]

A broadcast operation performed on the two interpolated arrays. Default: np.multiply.

kindstr

Interpolation type. See scipy.interpolate.interp1d. Default: "linear"

fill_valuefloat

The value to fill when extrapolating beyond the observed range. Default: 0

axisint

The axis of interpolation. Default: -2

Returns:
resultnp.ndarray or (np.ndarray, np.ndarray)

The result from combining both arrays after interpolation. If op is set to None, returns the interpolated arrays separately (y1, y2).

See also

librosa.feature.metrogram

Examples

>>> import numpy as np
>>>
>>> # two arrays of different lengths and sampling positions
>>> x1 = np.array([1, 1, 1])
>>> x1_pos = np.array([0, 0.5, 1])
>>> x2 = np.array([5, 10])
>>> x2_pos = np.array([0, 1])
>>>
>>> # interpolate to x1_pos and broadcast multiply (the defaults)
>>> product = librosa.util.interp_broadcast(
...     x1=x1,
...     x1_pos=x1_pos,
...     x2=x2,
...     x2_pos=x2_pos,
...     axis=0,
... )
>>>
>>> product
array([ 5. ,  7.5, 10. ])