MATLAB and Julia implementation of the Par-measure

In this repository you can find the MATLAB and Julia (not tested as well as the MATLAB version) code for a perceptual distortion measure based on auditory masking. Such a measure can predict if a human can notice the difference between two acoustic signals. In particular, this code reflects my interpretation of the distortion measure proposed by Van de Par et al. in [1]. In the following I will refer to it as the Par-measure. The major strength of the Par-measure is that, once the masker is fixed, it can be expressed as a weighted $l_2$ norm of the disturbance. This allows for incorporating the measure in optimization problems in which it is important to keep the computational-complexity limited.

Concretely, consider an actual acoustic signal $s$ and a reference acoustic signal $s^\star$. The difference between the two signals is $\epsilon=s-s^\star$. The Par-measure computes the distortion as

$$ D(s, \epsilon) = d. $$

If $d \leq 1$, it is predicted that a human observer can not notice the difference between $s$ and $s^\star=s-\epsilon$ in the presence of $s$. The acoustic signal $s$, which limits the audibility of the distortion, is called the masker. The Par-measure operates in the frequency-domain on short-time frames of about 20 to 40 ms [1].

This repository includes:

• A report REPORT.pdf which explains the background of the Par-measure, the functionality of the code and the provided examples;
• The MATLAB code par_measure.m which can be used to compute the masking curves;
• The Julia code Julia_version/par_measure.jl and Julia_version/test_par_measure.jl. This code is tested less well than the MATLAB version.
• The MATLAB code example1_basics.m, which shows the functionality of the code;
• The MATLAB code example2a_loudness_increase.m, which uses the Par-measure to increase the loudness of acoustic signals while keeping the perceived distortion limited. This example is directly based on the work done by Jeannerot et al. in [2] and, in my opinion, is a nice example of how to use the Par-measure inside an optimization framework;
• The MATLAB code example2b_hard_clipping.m, which uses hard clipping to perform the loudness increase of acoustic signals;
• The .wav files corresponding to example_2a_loudness_increase.m and example_2b_hard_clipping.m can be found in the Data folder. As reference files I used two different signals. The results of the first signal can be found in Data/Example_audio_1 and the results for the second signal are found in Data/Example_audio_2. The files loudness_hard_<>.wav correspond to hard clipping with parameter <>. The files loudness_percep_<>.wav correspond to using the Par-measure with parameter $d$ equal to <>.
  • I do not know an easy way to compare the two types of parameters, so the best approach is to listen to a few audio files and try to compare the perceived distortion and the perceived loudness increase.
  • Note that the maximum amplitude of the audio in each file is equal!

Contact

Feel free to leave a message in case you have questions, find mistakes, or have any other comments!

Dependencies

The code was tested on MATLAB R2023b and MATLAB R2024b on Ubuntu 23.10. I think the Par-measure can be used using default MATLAB functionality, but if I notice that certain packages are needed I will list them here. For Julia I used version 1.11.5.

To run Example 2, you need CVX. It should be straightforward to rewrite the examples to use other optimisation packages such as YALMIP or CVXPY, though the latter requires interfacing with Python.

Keywords

Acoustic signal processing, perceptual distortion, distortion measure, Par-measure, psychoacoustical modelling, auditory masking

Notes

• There is also a Python implementation by Niels de Koeijer (Bang & Olufsen)!! See link. This implementation can be used in PyTorch as a loss function.
• We used this implementation of the Par-measure in "Loudspeaker Beamforming to Enhance Speech Recognition Performance of Voice Driven Applications", to appear at ICASSP 2025, see [3].

Bibiliography

[1] van de Par, S., Kohlrausch, A., Heusdens, R. et al. A Perceptual Model for Sinusoidal Audio Coding Based on Spectral Integration. EURASIP J. Adv. Signal Process. 2005, 317529 (2005). DOI

[2] A. Jeannerot, N. de Koeijer, P. Martínez-Nuevo, M. B. Møller, J. Dyreby and P. Prandoni, "Increasing Loudness in Audio Signals: A Perceptually Motivated Approach to Preserve Audio Quality," ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Singapore, Singapore, 2022, pp. 1001-1005. https://doi.org/10.1109/ICASSP43922.2022.9747589. Alternative ARXIV link.

[3] Dimme de Groot, Baturalp Karslioglu, Odette Scharenborg and Jorge Martinez, "Loudspeaker Beamforming to Enhance Speech Recognition Performance of Voice Driven Applications", 2025. ARXIV preprint