torchlpc 0.2

Fast, efficient, and differentiable time-varying LPC filtering in PyTorch.

TorchLPC

torchlpc provides a PyTorch implementation of the Linear Predictive Coding (LPC) filtering operation, also known as IIR filtering. It's fast, differentiable, and supports batched inputs with time-varying filter coefficients. The computation is done as follows:

Given an input signal $\mathbf{x} \in \mathbb{R}^T$ and time-varying LPC coefficients $\mathbf{A} \in \mathbb{R}^{T \times N}$ with an order of $N$, the LPC filtering operation is defined as:

\mathbf{y}_t = \mathbf{x}_t - \sum_{i=1}^N \mathbf{A}_{t,i} \mathbf{y}_{t-i}.

It's still in early development, so please open an issue if you find any bugs.

Usage

import torch
from torchlpc import sample_wise_lpc

# Create a batch of 10 signals, each with 100 time steps
x = torch.randn(10, 100)

# Create a batch of 10 sets of LPC coefficients, each with 100 time steps and an order of 3
A = torch.randn(10, 100, 3)

# Apply LPC filtering
y = sample_wise_lpc(x, A)

# Optionally, you can provide initial values for the output signal (default is 0)
zi = torch.randn(10, 3)
y = sample_wise_lpc(x, A, zi=zi)

Installation

pip install torchlpc

or from source

pip install git+https://github.com/yoyololicon/torchlpc.git

Derivation of the gradients of the LPC filtering operation

Will (not) be added soon... I'm not good at math :sweat_smile:. But the implementation passed both gradcheck and gradgradcheck tests, so I think it's 99.99% correct and workable :laughing:. The algorithm is extended from my recent paper GOLF[^1].

[^1]: Singing Voice Synthesis Using Differentiable LPC and Glottal-Flow-Inspired Wavetables.

TODO

• Use PyTorch C++ extension for faster computation.
• Use native CUDA kernels for GPU computation.
• Add examples.

Citation

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

@software{torchlpc,
  author = {Chin-Yun Yu},
  title = {{TorchLPC}: fast, efficient, and differentiable time-varying {LPC} filtering in {PyTorch}},
  year = {2023},
  version = {0.1.0},
  url = {https://github.com/yoyololicon/torchlpc},
}