Warped linear predictive coding (warped LPC or WLPC) is a variant of linear predictive coding in which the spectral representation of the system is modified, for example by replacing the unit delays used in an LPC implementation with first-order allpass filters. This can have advantages in reducing the bitrate required for a given level of perceived audio quality/intelligibility, especially in wideband audio coding.
https://en.wikipedia.org/wiki/Warped_linear_predictive_coding
This repository contains an introduction to warped linear prediction through Jupyter notebooks in the gh-pages branch, viewable at https://sevagh.github.io/warped-linear-prediction.
WLPAC, or "Warped Linear Prediction Audio Codec", is an audio codec. In this repository I use wlpac to refer to an experimental new audio file format based on the WLPC residual in a FLAC container - files are stored with the extension .wlp.flac.
Input files should be uncompressed WAV files. Space savings are measured compared to the original WAV file, and the PESQ and spectrogram are taken straight from the .wlp.flac file.
You can play .wlp.flac files with any media player, e.g. mpv, making this a well-suited general purpose audio codec.
Every implementation starts at stage 1, using WLP to find the residual signal, which should be a smaller signal than the original. Optional parameters to stage 1 are the quantization ratio, and Huffman encoding. This is followed by a pass at stage 2 to store the residual using FLAC as a container.
Decompression is done by extracing the residual signal from the FLAC container and reconstructing the original signal by reversing the Warped FIR procedure.
Compression results with filesizes for WLPAC and regular FLAC:
| File | WLPAC compression (%) | WLPAC PESQ* | FLAC compression** (%) | FLAC PESQ |
|---|---|---|---|---|
| english_m | 65 | 4.50 | 67 | 4.55 |
| english_f | 67 | 4.52 | 69 | 4.55 |
| french_m | 66 | 4.51 | 70 | 4.55 |
| french_f | 64 | 4.53 | 68 | 4.55 |
*: quality is calculated with PESQ, Perceptual Evaluation of Speech Quality. The results are given for 4 clips, 2 male and 2 female speech clips (English and French) with the maximum possible PESQ of 4.5, taken from https://www.signalogic.com/index.pl?page=speech_codec_wav_samples and included in the samples dir.
**: FLAC compression without WLP tested with ffmpeg
Note the extra space savings over regular FLAC compression with a small hit in quality. In my personal listening tests, I don't notice a difference.
| Original | WLPAC | FLAC |
|---|---|---|
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On the master branch, there is a Python 3 package, wlpac, which contains a library and some command line tools for working with wlpac:
wlpac_encode- convert a WAV file to a wlpac file, with your choice of stage 2 containerwlpac_decode- convert a wlpac file to a WAV filewlpac_compare- output a PESQ score and spectrogram from input audio files ('.wlp.flac' supported)
There's a setup.py and requirements.txt file. Everything has been verified to work on Python 3.8.
In the original Jupyter notebooks, I used several compression techniques, including quantization, Huffman encoding, lzma and pickle to create custom file formats for the WLPAC (similar to https://github.com/sevagh/quadtree-compression). After further (unsuccessful) experimentation with other data compression algorithms include bz2 and zlib, I changed track to rely on a real audio codec, FLAC, as a container for the WLPC residual.