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librosa.core.lpc¶

librosa.core.lpc(y, order)[source]¶

Linear Prediction Coefficients via Burg’s method

This function applies Burg’s method to estimate coefficients of a linear filter on y of order order. Burg’s method is an extension to the Yule-Walker approach, which are both sometimes referred to as LPC parameter estimation by autocorrelation.

It follows the description and implementation approach described in the introduction in [1]. N.B. This paper describes a different method, which is not implemented here, but has been chosen for its clear explanation of Burg’s technique in its introduction.

1: Larry Marple A New Autoregressive Spectrum Analysis Algorithm IEEE Transactions on Accoustics, Speech, and Signal Processing vol 28, no. 4, 1980

Parameters

ynp.ndarray: Time series to fit
orderint > 0: Order of the linear filter

Returns

anp.ndarray of length order + 1: LP prediction error coefficients, i.e. filter denominator polynomial

Raises

ParameterError

If y is not valid audio as per util.valid_audio
If order < 1 or not integer

FloatingPointError

If y is ill-conditioned

See also

scipy.signal.lfilter

Examples

Compute LP coefficients of y at order 16 on entire series

>>> y, sr = librosa.load(librosa.util.example_audio_file(), offset=30,
...                      duration=10)
>>> librosa.lpc(y, 16)

Compute LP coefficients, and plot LP estimate of original series

>>> import matplotlib.pyplot as plt
>>> import scipy
>>> y, sr = librosa.load(librosa.util.example_audio_file(), offset=30,
...                      duration=0.020)
>>> a = librosa.lpc(y, 2)
>>> y_hat = scipy.signal.lfilter([0] + -1*a[1:], [1], y)
>>> plt.figure()
>>> plt.plot(y)
>>> plt.plot(y_hat, linestyle='--')
>>> plt.legend(['y', 'y_hat'])
>>> plt.title('LP Model Forward Prediction')
>>> plt.show()