Phase Intercept Distortion

Introduction

Phase distortion refers to the alteration of the phase relationships between frequencies in a signal, which can be perceptible. Phase intercept distortion is a form of phase distortion, created by an operation called the frequency-independent phase shift. The transfer function of a frequency-independent phase shift of $\theta$ is defined as:

$$ |H(\omega)|= 1 $$

$$ \angle H(\omega) = \theta \cdot sgn(\omega) $$

where $\theta$ is the phase intercept shift angle, and $sgn(\omega)$ is the signum function of the frequency $\omega$. In simpler words, this means that the phase of each frequency component is shifted by a constant angle $\theta$, regardless of its frequency, leaving the amplitude unchanged.

Overview

The paper, The Perception of Phase Intercept Distortion and its Application in Data Augmentation, presents evidence through human subject experiments that the special case of phase-intercept distortion is not perceptible in real-world sounds, although this form of distortion changes a signal’s waveform significantly. The paper also describes how this fact can be leveraged for data augmentation in audio-based machine learning applications.

This repository implements the frequency-independent phase shift operation to introduce phase intercept distortion, which can be used for data augmentation in audio-based machine learning applications. It provides a numpy and torch implementation of applying this phase intercept distortion to -

1. Single audio array in numpy
2. Batch of training samples in torch for data augmentation

Example Usage

Prior to testing, we recommend creating a virtual environment, and then run -

pip install -r requirements.txt

This will install the required dependencies for the project.

Phase Intercept Distortion examples

We have added some example audios from AudioSet in the directory: examples/originals. These example data samples are made available by Google Inc. under a Creative Commons Attribution 4.0 International (CC BY 4.0) license. To test the effect of phase intercept distortion on these samples, run -

python generate-examples.py

• The modified/distorted audio will be saved inside the examples/distorted directory.
• The original and distorted audio plots will be saved inside examples/plots as .png files.

Applying Phase Intercept Distortion to a single audio

To apply phase intercept distortion to your own audio files, use:

python augmentation.py /PATH/to/audio.wav /PATH/to/output/directory

This will apply the Hilbert Transform by default (phase intercept distortion with $\theta = -\pi/2$) to the audio file and save the augmented audio in the specified output directory. If you want to use a different phase intercept distortion angle, you can specify it using the --theta flag:

python augmentation.py /PATH/to/audio.wav /PATH/to/output/directory --theta <angle_in_radians>

Applying Phase Intercept Distortion for Data Augmentation (PyTorch)

To use phase intercept distortion for data augmentation in a PyTorch training pipeline, you can integrate the PhaseInterceptDistortion module into your script. Here's an example of how to do this:

import torch
import numpy as np
from augmentation import PhaseInterceptDistortion

# Initialize the module
pid = PhaseInterceptDistortion()

# Example input tensor (batch_size, channels, samples)
audio = torch.randn(4, 1, 16000)

# Apply phase intercept distortion
augmented_audio = pid(audio)

This will apply the random phase intercept distortion to the input audio tensor. The random angle is sampled uniformly from the range [-π, π] for each audio sample in the batch. You can also specify a custom phase intercept distortion angle by passing a theta tensor to the forward method.

# Example custom theta tensor (batch_size,)
theta = torch.tensor([-np.pi/2, 0, np.pi/2, np.pi/4])

# Apply phase intercept distortion with custom theta
augmented_audio = pid(audio, theta=theta)