Confusion about how to use LPC, and the Numerical Error it gives

Describe the bug I don’t understand what the Numerical error, input ill-conditioned?" error means in the LPC function, and I also find the documentation a bit confusing, as it doesn’t really specify how I can use the LPC function.

To Reproduce

import numpy as np
import librosa

y = np.sin(np.arange(100) * 0.1) * 0.1

y_hat = librosa.lpc(y, 16) # throws said error here

Software versions*

>>> import platform; print(platform.platform())
Windows-10-10.0.19041-SP0
>>> import sys; print("Python", sys.version)
Python 3.7.4 (tags/v3.7.4:e09359112e, Jul  8 2019, 20:34:20) [MSC v.1916 64 bit (AMD64)]
>>> import numpy; print("NumPy", numpy.__version__)
NumPy 1.17.0
>>> import scipy; print("SciPy", scipy.__version__)
SciPy 1.4.1
>>> import librosa; print("librosa", librosa.__version__)
librosa 0.7.1
>>> 
>>> librosa.show_versions()
INSTALLED VERSIONS
------------------
python: 3.7.4 (tags/v3.7.4:e09359112e, Jul  8 2019, 20:34:20) [MSC v.1916 64 bit (AMD64)]

librosa: 0.7.1

audioread: 2.1.8
numpy: 1.17.0
scipy: 1.4.1
sklearn: 0.22
joblib: 0.14.1
decorator: 4.4.1
six: 1.12.0
soundfile: 0.10.3
resampy: 0.2.2
numba: 0.46.0

numpydoc: None
sphinx: None
sphinx_rtd_theme: None
sphinxcontrib.versioning: None
sphinx-gallery: None
pytest: None
pytest-mpl: None
pytest-cov: None
matplotlib: 3.1.2
presets: None

Additional context I’m trying to use LPC to resynthesize speech from a given audio sample, however I struggle to understand how I should do this and how I have to use LPC in general. From what I understand from here: https://www.fon.hum.uva.nl/rob/VocalTractExamples/ It’s possible to use LPC to get the filter coefficients for source-filter synthesis, which is what I’m tying to do.

[ajweiss]

Incidentally, it’s long been on my todo list to put together an example notebook that demos source filter separation and synthesis by analysis using LPC, maybe it’s time to pick that back up…

[ajweiss]

In terms of analysis, I have a branch (https://github.com/ajweiss/librosa/tree/lpcspec) that implements both a short time LPC transform (windowed LPC coeffs) and also a function that then takes those coefficients and computes their spectrum. It hasn’t been touched in quite a while, but is a pretty good start (I think) on the analysis side of things. What were you thinking in terms of analysis? I’ve been thinking about dusting this off for quite some time.

I’d also be interested in collaborating on examples. In general I was considering LPC spectral analysis and perhaps a basic compression demo… What did you have in mind?