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add reference to interspeech paper
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yoyolicoris committed Jun 10, 2024
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## Derivation of the gradients of the LPC filter

The details of the derivation can be found in our preprint **Differentiable All-pole Filters for Time-varying Audio Systems**[^1].
The details of the derivation can be found in our preprints[^1][^2].
We show that, given the instataneous gradient $\frac{\partial \mathcal{L}}{\partial y_t}$ where $\mathcal{L}$ is the loss function, the gradients of the LPC filter with respect to the input signal $\bf x$ and the filter coefficients $\bf A$ can be expresssed also through a time-varying filter:

```math
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\end{vmatrix}.
$$

This algorithm is more efficient than [^2] because it only needs one pass of filtering to get the two gradients while the latter needs two.
This algorithm is more efficient than [^3] because it only needs one pass of filtering to get the two gradients while the latter needs two.

[^1]: [Differentiable All-pole Filters for Time-varying Audio Systems](https://arxiv.org/abs/2404.07970).
[^2]: [Singing Voice Synthesis Using Differentiable LPC and Glottal-Flow-Inspired Wavetables](https://arxiv.org/abs/2306.17252).
[^2]: [Differentiable Time-Varying Linear Prediction in the Context of End-to-End Analysis-by-Synthesis](https://arxiv.org/abs/2406.05128).
[^3]: [Singing Voice Synthesis Using Differentiable LPC and Glottal-Flow-Inspired Wavetables](https://arxiv.org/abs/2306.17252).

## TODO

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## Citation

If you find this repository useful in your research, please cite our work with the following BibTex entry:
If you find this repository useful in your research, please cite our work with the following BibTex entries:

```bibtex
@misc{ycy2024diffapf,
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archivePrefix={arXiv},
primaryClass={eess.AS}
}
@misc{ycy2024golf,
title = {Differentiable Time-Varying Linear Prediction in the Context of End-to-End Analysis-by-Synthesis},
author = {Yu, Chin-Yun and Fazekas, György},
year={2024},
eprint={2406.05128},
archivePrefix={arXiv},
primaryClass={eess.AS}
}
```

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