vqt 0.1.2

Variable Q-Transform with PyTorch backend

VQT: Variable Q-Transform

Contributions are welcome! Feel free to open an issue or a pull request.

Variable Q-Transform

This is a novel python implementation of the variable Q-transform that was developed due to the need for a more accurate and flexible VQT for the use in research. It is battle-tested and has been used in a number of research projects.

• Accuracy: The approach is different in that it is a direct implementation of a spectrogram via a Hilbert transformation at each desired frequency. This results in an exact computation of the spectrogram and is appropriate for research applications where accuracy is critical. The implementation seen in librosa and nnAudio uses recursive downsampling, which can introduce artifacts in the spectrogram under certain conditions.
• Flexibility: The parameters and codebase are less complex than in other libraries, and the filter bank is fully customizable and exposed to the user. Built in plotting of the filter bank makes tuning the parameters easy and intuitive.
• Speed: The backend is written using PyTorch, and allows for GPU acceleration. It is faster than the librosa implementation under most cases, and roughly as fast as the nnAudio implementation. See below section 'What to improve on?' for more details on how to speed it up further.

Installation

From PyPI: pip install vqt

From source:

git clone https://github.com/RichieHakim/vqt.git
cd vqt
pip install -e .

Requirements: torch, numpy, scipy, matplotlib, tqdm
These will be installed automatically if you install from PyPI.

Usage

import vqt

signal = X  ## numpy or torch array of shape (n_channels, n_samples)

transformer = vqt.VQT(
    Fs_sample=1000,  ## In Hz
    Q_lowF=3,  ## In periods per octave
    Q_highF=20,  ## In periods per octave
    F_min=10,  ## In Hz
    F_max=400,  ## In Hz
    n_freq_bins=55,  ## Number of frequency bins
    DEVICE_compute='cpu',
    return_complex=False,
    filters=None,  ## Use custom filters
    plot_pref=False,  ## Can show the filter bank
)

spectrograms, x_axis, frequencies = transformer(signal)

What is the Variable Q-Transform?

The Variable Q-Transform (VQT) is a time-frequency analysis tool that generates spectrograms, similar to the Short-time Fourier Transform (STFT). It can also be defined as a special case of a wavelet transform, as well as the generalization of the Constant Q-Transform (CQT). In fact, the VQT subsumes the CQT and STFT as both can be recreated using specific parameters of the VQT.

Why use the VQT?

It provides enough knobs to tune the time-frequency resolution trade-off to suit your needs.

How exactly does this implementation differ from others?

This function works differently than the VQT from librosa or nnAudio in that it does not use the recursive downsampling algorithm from this paper. Instead, it computes the power at each frequency using either direct- or FFT-convolution with a filter bank of complex oscillations, followed by a Hilbert transform. This results in a more accurate computation of the same spectrogram. The direct computation approach also results in code that is more flexible, easier to understand, and it has fewer constraints on the input parameters compared to librosa and nnAudio.

What to improve on?

Contributions are welcome! Feel free to open an issue or a pull request.

• Flexibility:

  • librosa parameter mode: It would be nice to have a mode that allows for the same parameters as librosa to be used.
  • Make VQT class a full torch.nn.Module so that it can be used in a torch.nn.Sequential model. Ensure backpropagation works.
  • Make VQT class compatible with torch.jit.script and torch.jit.trace.

• Speed:

  • Lossless approaches:
    • For the fft_conv approach: I believe a massive (5-100x) speedup is possible using a sparse or non-uniform FFT. A direct approach where only the non-zero frequencies are computed in the fft, product, and ifft should get us closer to a theoretically optimal lossless approach. There is an implmentation of the NUFFT in PyTorch here.
    • For the conv1d approach: I think it would be much faster if we cropped the filters to remove the blank space from the higher frequency filters. This would be pretty easy to implement and could give a >10x speedup.
  • Lossy approaches:
    • Recursive downsampling: Under many circumstances (like when Q_high is not much greater than Q_low), recursive downsampling is fine. Implementing it would be nice just for completeness (from this paper)
    • For conv1d approach: Use a strided convolution.
    • For fftconv approach: Downsample using n=n_samples_downsampled in ifft function.
  • Non-trivial ideas that theoretically could speed things up:
    • An FFT implementation that allows for a reduced set of frequencies to be computed.

Demo:

import vqt
import numpy as np
import torch
import matplotlib.pyplot as plt
import scipy

data_ecg = torch.as_tensor(scipy.datasets.electrocardiogram()[:10000])
sample_rate = 360

my_vqt = vqt.VQT(
    Fs_sample=sample_rate,
    Q_lowF=2,
    Q_highF=8,
    F_min=1,
    F_max=120,
    n_freq_bins=150,
    win_size=1501,
    window_type='gaussian',
    downsample_factor=8,
    padding='same',
    fft_conv=True,
    take_abs=True,
    plot_pref=False,
)

specs, xaxis, freqs = my_vqt(data_ecg)

fig, axs = plt.subplots(nrows=2, ncols=1, sharex=True, )
axs[0].plot(np.arange(data_ecg.shape[0]) / sample_rate, data_ecg)
axs[0].title.set_text('Electrocardiogram')
axs[1].pcolor(
    xaxis / sample_rate, 
    np.arange(specs[0].shape[0]), specs[0] * (freqs)[:, None], 
    vmin=0, 
    vmax=30,
    cmap='hot',
)
axs[1].set_yticks(np.arange(specs.numpy()[0].shape[0])[::10], np.round(freqs.numpy()[::10], 1));
axs[1].set_xlim([13, 22])
axs[0].set_ylabel('mV')
axs[1].set_ylabel('frequency (Hz)')
axs[1].set_xlabel('time (s)')
plt.show()