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Audio Resampling

Here, we will walk through resampling audio waveforms using torchaudio.

# When running this tutorial in Google Colab, install the required packages
# with the following.
# !pip install torchaudio librosa

import torch
import torchaudio
import torchaudio.functional as F
import torchaudio.transforms as T

print(torch.__version__)
print(torchaudio.__version__)

Out:

1.10.0+cu102
0.10.0+cu102

Preparing data and utility functions (skip this section)

#@title Prepare data and utility functions. {display-mode: "form"}
#@markdown
#@markdown You do not need to look into this cell.
#@markdown Just execute once and you are good to go.

#-------------------------------------------------------------------------------
# Preparation of data and helper functions.
#-------------------------------------------------------------------------------

import math
import time

import librosa
import matplotlib.pyplot as plt
from IPython.display import Audio, display
import pandas as pd


DEFAULT_OFFSET = 201
SWEEP_MAX_SAMPLE_RATE = 48000
DEFAULT_LOWPASS_FILTER_WIDTH = 6
DEFAULT_ROLLOFF = 0.99
DEFAULT_RESAMPLING_METHOD = 'sinc_interpolation'


def _get_log_freq(sample_rate, max_sweep_rate, offset):
  """Get freqs evenly spaced out in log-scale, between [0, max_sweep_rate // 2]

  offset is used to avoid negative infinity `log(offset + x)`.

  """
  half = sample_rate // 2
  start, stop = math.log(offset), math.log(offset + max_sweep_rate // 2)
  return torch.exp(torch.linspace(start, stop, sample_rate, dtype=torch.double)) - offset

def _get_inverse_log_freq(freq, sample_rate, offset):
  """Find the time where the given frequency is given by _get_log_freq"""
  half = sample_rate // 2
  return sample_rate * (math.log(1 + freq / offset) / math.log(1 + half / offset))

def _get_freq_ticks(sample_rate, offset, f_max):
  # Given the original sample rate used for generating the sweep,
  # find the x-axis value where the log-scale major frequency values fall in
  time, freq = [], []
  for exp in range(2, 5):
    for v in range(1, 10):
      f = v * 10 ** exp
      if f < sample_rate // 2:
        t = _get_inverse_log_freq(f, sample_rate, offset) / sample_rate
        time.append(t)
        freq.append(f)
  t_max = _get_inverse_log_freq(f_max, sample_rate, offset) / sample_rate
  time.append(t_max)
  freq.append(f_max)
  return time, freq

def get_sine_sweep(sample_rate, offset=DEFAULT_OFFSET):
  max_sweep_rate = sample_rate
  freq = _get_log_freq(sample_rate, max_sweep_rate, offset)
  delta = 2 * math.pi * freq / sample_rate
  cummulative = torch.cumsum(delta, dim=0)
  signal = torch.sin(cummulative).unsqueeze(dim=0)
  return signal

def plot_sweep(waveform, sample_rate, title, max_sweep_rate=SWEEP_MAX_SAMPLE_RATE, offset=DEFAULT_OFFSET):
  x_ticks = [100, 500, 1000, 5000, 10000, 20000, max_sweep_rate // 2]
  y_ticks = [1000, 5000, 10000, 20000, sample_rate//2]

  time, freq = _get_freq_ticks(max_sweep_rate, offset, sample_rate // 2)
  freq_x = [f if f in x_ticks and f <= max_sweep_rate // 2 else None for f in freq]
  freq_y = [f for f in freq if f >= 1000 and f in y_ticks and f <= sample_rate // 2]

  figure, axis = plt.subplots(1, 1)
  axis.specgram(waveform[0].numpy(), Fs=sample_rate)
  plt.xticks(time, freq_x)
  plt.yticks(freq_y, freq_y)
  axis.set_xlabel('Original Signal Frequency (Hz, log scale)')
  axis.set_ylabel('Waveform Frequency (Hz)')
  axis.xaxis.grid(True, alpha=0.67)
  axis.yaxis.grid(True, alpha=0.67)
  figure.suptitle(f'{title} (sample rate: {sample_rate} Hz)')
  plt.show(block=True)

def play_audio(waveform, sample_rate):
  waveform = waveform.numpy()

  num_channels, num_frames = waveform.shape
  if num_channels == 1:
    display(Audio(waveform[0], rate=sample_rate))
  elif num_channels == 2:
    display(Audio((waveform[0], waveform[1]), rate=sample_rate))
  else:
    raise ValueError("Waveform with more than 2 channels are not supported.")

def plot_specgram(waveform, sample_rate, title="Spectrogram", xlim=None):
  waveform = waveform.numpy()

  num_channels, num_frames = waveform.shape
  time_axis = torch.arange(0, num_frames) / sample_rate

  figure, axes = plt.subplots(num_channels, 1)
  if num_channels == 1:
    axes = [axes]
  for c in range(num_channels):
    axes[c].specgram(waveform[c], Fs=sample_rate)
    if num_channels > 1:
      axes[c].set_ylabel(f'Channel {c+1}')
    if xlim:
      axes[c].set_xlim(xlim)
  figure.suptitle(title)
  plt.show(block=False)

def benchmark_resample(
    method,
    waveform,
    sample_rate,
    resample_rate,
    lowpass_filter_width=DEFAULT_LOWPASS_FILTER_WIDTH,
    rolloff=DEFAULT_ROLLOFF,
    resampling_method=DEFAULT_RESAMPLING_METHOD,
    beta=None,
    librosa_type=None,
    iters=5
):
  if method == "functional":
    begin = time.time()
    for _ in range(iters):
      F.resample(waveform, sample_rate, resample_rate, lowpass_filter_width=lowpass_filter_width,
                 rolloff=rolloff, resampling_method=resampling_method)
    elapsed = time.time() - begin
    return elapsed / iters
  elif method == "transforms":
    resampler = T.Resample(sample_rate, resample_rate, lowpass_filter_width=lowpass_filter_width,
                           rolloff=rolloff, resampling_method=resampling_method, dtype=waveform.dtype)
    begin = time.time()
    for _ in range(iters):
      resampler(waveform)
    elapsed = time.time() - begin
    return elapsed / iters
  elif method == "librosa":
    waveform_np = waveform.squeeze().numpy()
    begin = time.time()
    for _ in range(iters):
      librosa.resample(waveform_np, sample_rate, resample_rate, res_type=librosa_type)
    elapsed = time.time() - begin
    return elapsed / iters

To resample an audio waveform from one freqeuncy to another, you can use transforms.Resample or functional.resample. transforms.Resample precomputes and caches the kernel used for resampling, while functional.resample computes it on the fly, so using transforms.Resample will result in a speedup when resampling multiple waveforms using the same parameters (see Benchmarking section).

Both resampling methods use bandlimited sinc interpolation to compute signal values at arbitrary time steps. The implementation involves convolution, so we can take advantage of GPU / multithreading for performance improvements. When using resampling in multiple subprocesses, such as data loading with multiple worker processes, your application might create more threads than your system can handle efficiently. Setting torch.set_num_threads(1) might help in this case.

Because a finite number of samples can only represent a finite number of frequencies, resampling does not produce perfect results, and a variety of parameters can be used to control for its quality and computational speed. We demonstrate these properties through resampling a logarithmic sine sweep, which is a sine wave that increases exponentially in frequency over time.

The spectrograms below show the frequency representation of the signal, where the x-axis corresponds to the frequency of the original waveform (in log scale), y-axis the frequency of the plotted waveform, and color intensity the amplitude.

sample_rate = 48000
resample_rate = 32000

waveform = get_sine_sweep(sample_rate)
plot_sweep(waveform, sample_rate, title="Original Waveform")
play_audio(waveform, sample_rate)

resampler = T.Resample(sample_rate, resample_rate, dtype=waveform.dtype)
resampled_waveform = resampler(waveform)
plot_sweep(resampled_waveform, resample_rate, title="Resampled Waveform")
play_audio(waveform, sample_rate)
  • ../_images/sphx_glr_audio_resampling_tutorial_001.png
  • ../_images/sphx_glr_audio_resampling_tutorial_002.png

Out:

<IPython.lib.display.Audio object>
<IPython.lib.display.Audio object>

Controling resampling quality with parameters

Lowpass filter width

Because the filter used for interpolation extends infinitely, the lowpass_filter_width parameter is used to control for the width of the filter to use to window the interpolation. It is also referred to as the number of zero crossings, since the interpolation passes through zero at every time unit. Using a larger lowpass_filter_width provides a sharper, more precise filter, but is more computationally expensive.

sample_rate = 48000
resample_rate = 32000

resampled_waveform = F.resample(waveform, sample_rate, resample_rate, lowpass_filter_width=6)
plot_sweep(resampled_waveform, resample_rate, title="lowpass_filter_width=6")

resampled_waveform = F.resample(waveform, sample_rate, resample_rate, lowpass_filter_width=128)
plot_sweep(resampled_waveform, resample_rate, title="lowpass_filter_width=128")
  • ../_images/sphx_glr_audio_resampling_tutorial_003.png
  • ../_images/sphx_glr_audio_resampling_tutorial_004.png

Rolloff

The rolloff parameter is represented as a fraction of the Nyquist frequency, which is the maximal frequency representable by a given finite sample rate. rolloff determines the lowpass filter cutoff and controls the degree of aliasing, which takes place when frequencies higher than the Nyquist are mapped to lower frequencies. A lower rolloff will therefore reduce the amount of aliasing, but it will also reduce some of the higher frequencies.

sample_rate = 48000
resample_rate = 32000

resampled_waveform = F.resample(waveform, sample_rate, resample_rate, rolloff=0.99)
plot_sweep(resampled_waveform, resample_rate, title="rolloff=0.99")

resampled_waveform = F.resample(waveform, sample_rate, resample_rate, rolloff=0.8)
plot_sweep(resampled_waveform, resample_rate, title="rolloff=0.8")
  • ../_images/sphx_glr_audio_resampling_tutorial_005.png
  • ../_images/sphx_glr_audio_resampling_tutorial_006.png

Window function

By default, torchaudio’s resample uses the Hann window filter, which is a weighted cosine function. It additionally supports the Kaiser window, which is a near optimal window function that contains an additional beta parameter that allows for the design of the smoothness of the filter and width of impulse. This can be controlled using the resampling_method parameter.

sample_rate = 48000
resample_rate = 32000

resampled_waveform = F.resample(waveform, sample_rate, resample_rate, resampling_method="sinc_interpolation")
plot_sweep(resampled_waveform, resample_rate, title="Hann Window Default")

resampled_waveform = F.resample(waveform, sample_rate, resample_rate, resampling_method="kaiser_window")
plot_sweep(resampled_waveform, resample_rate, title="Kaiser Window Default")
  • ../_images/sphx_glr_audio_resampling_tutorial_007.png
  • ../_images/sphx_glr_audio_resampling_tutorial_008.png

Comparison against librosa

torchaudio’s resample function can be used to produce results similar to that of librosa (resampy)’s kaiser window resampling, with some noise

sample_rate = 48000
resample_rate = 32000

### kaiser_best
resampled_waveform = F.resample(
    waveform,
    sample_rate,
    resample_rate,
    lowpass_filter_width=64,
    rolloff=0.9475937167399596,
    resampling_method="kaiser_window",
    beta=14.769656459379492
)
plot_sweep(resampled_waveform, resample_rate, title="Kaiser Window Best (torchaudio)")

librosa_resampled_waveform = torch.from_numpy(
    librosa.resample(waveform.squeeze().numpy(), sample_rate, resample_rate, res_type='kaiser_best')).unsqueeze(0)
plot_sweep(librosa_resampled_waveform, resample_rate, title="Kaiser Window Best (librosa)")

mse = torch.square(resampled_waveform - librosa_resampled_waveform).mean().item()
print("torchaudio and librosa kaiser best MSE:", mse)

### kaiser_fast
resampled_waveform = F.resample(
    waveform,
    sample_rate,
    resample_rate,
    lowpass_filter_width=16,
    rolloff=0.85,
    resampling_method="kaiser_window",
    beta=8.555504641634386
)
plot_specgram(resampled_waveform, resample_rate, title="Kaiser Window Fast (torchaudio)")

librosa_resampled_waveform = torch.from_numpy(
    librosa.resample(waveform.squeeze().numpy(), sample_rate, resample_rate, res_type='kaiser_fast')).unsqueeze(0)
plot_sweep(librosa_resampled_waveform, resample_rate, title="Kaiser Window Fast (librosa)")

mse = torch.square(resampled_waveform - librosa_resampled_waveform).mean().item()
print("torchaudio and librosa kaiser fast MSE:", mse)
  • ../_images/sphx_glr_audio_resampling_tutorial_009.png
  • ../_images/sphx_glr_audio_resampling_tutorial_010.png
  • ../_images/sphx_glr_audio_resampling_tutorial_011.png
  • ../_images/sphx_glr_audio_resampling_tutorial_012.png

Out:

torchaudio and librosa kaiser best MSE: 2.080690115365992e-06
torchaudio and librosa kaiser fast MSE: 2.5200744248601027e-05

Performance Benchmarking

Below are benchmarks for downsampling and upsampling waveforms between two pairs of sampling rates. We demonstrate the performance implications that the lowpass_filter_wdith, window type, and sample rates can have. Additionally, we provide a comparison against librosa’s kaiser_best and kaiser_fast using their corresponding parameters in torchaudio.

To elaborate on the results:

  • a larger lowpass_filter_width results in a larger resampling kernel, and therefore increases computation time for both the kernel computation and convolution
  • using kaiser_window results in longer computation times than the default sinc_interpolation because it is more complex to compute the intermediate window values - a large GCD between the sample and resample rate will result in a simplification that allows for a smaller kernel and faster kernel computation.
configs = {
    "downsample (48 -> 44.1 kHz)": [48000, 44100],
    "downsample (16 -> 8 kHz)": [16000, 8000],
    "upsample (44.1 -> 48 kHz)": [44100, 48000],
    "upsample (8 -> 16 kHz)": [8000, 16000],
}

for label in configs:
  times, rows = [], []
  sample_rate = configs[label][0]
  resample_rate = configs[label][1]
  waveform = get_sine_sweep(sample_rate)

  # sinc 64 zero-crossings
  f_time = benchmark_resample("functional", waveform, sample_rate, resample_rate, lowpass_filter_width=64)
  t_time = benchmark_resample("transforms", waveform, sample_rate, resample_rate, lowpass_filter_width=64)
  times.append([None, 1000 * f_time, 1000 * t_time])
  rows.append(f"sinc (width 64)")

  # sinc 6 zero-crossings
  f_time = benchmark_resample("functional", waveform, sample_rate, resample_rate, lowpass_filter_width=16)
  t_time = benchmark_resample("transforms", waveform, sample_rate, resample_rate, lowpass_filter_width=16)
  times.append([None, 1000 * f_time, 1000 * t_time])
  rows.append(f"sinc (width 16)")

  # kaiser best
  lib_time = benchmark_resample("librosa", waveform, sample_rate, resample_rate, librosa_type="kaiser_best")
  f_time = benchmark_resample(
      "functional",
      waveform,
      sample_rate,
      resample_rate,
      lowpass_filter_width=64,
      rolloff=0.9475937167399596,
      resampling_method="kaiser_window",
      beta=14.769656459379492)
  t_time = benchmark_resample(
      "transforms",
      waveform,
      sample_rate,
      resample_rate,
      lowpass_filter_width=64,
      rolloff=0.9475937167399596,
      resampling_method="kaiser_window",
      beta=14.769656459379492)
  times.append([1000 * lib_time, 1000 * f_time, 1000 * t_time])
  rows.append(f"kaiser_best")

  # kaiser fast
  lib_time = benchmark_resample("librosa", waveform, sample_rate, resample_rate, librosa_type="kaiser_fast")
  f_time = benchmark_resample(
      "functional",
      waveform,
      sample_rate,
      resample_rate,
      lowpass_filter_width=16,
      rolloff=0.85,
      resampling_method="kaiser_window",
      beta=8.555504641634386)
  t_time = benchmark_resample(
      "transforms",
      waveform,
      sample_rate,
      resample_rate,
      lowpass_filter_width=16,
      rolloff=0.85,
      resampling_method="kaiser_window",
      beta=8.555504641634386)
  times.append([1000 * lib_time, 1000 * f_time, 1000 * t_time])
  rows.append(f"kaiser_fast")

  df = pd.DataFrame(times,
                    columns=["librosa", "functional", "transforms"],
                    index=rows)
  df.columns = pd.MultiIndex.from_product([[f"{label} time (ms)"],df.columns])
  display(df.round(2))

Out:

downsample (48 -> 44.1 kHz) time (ms)
                                              librosa functional transforms
sinc (width 64)                                   NaN      19.30       0.43
sinc (width 16)                                   NaN      17.70       0.39
kaiser_best                                     61.33      27.51       0.43
kaiser_fast                                      9.83      25.81       0.39
                downsample (16 -> 8 kHz) time (ms)
                                           librosa functional transforms
sinc (width 64)                                NaN       1.63       0.80
sinc (width 16)                                NaN       0.54       0.33
kaiser_best                                  21.74       1.16       0.83
kaiser_fast                                   4.29       0.64       0.35
                upsample (44.1 -> 48 kHz) time (ms)
                                            librosa functional transforms
sinc (width 64)                                 NaN      19.86       0.45
sinc (width 16)                                 NaN      18.33       0.40
kaiser_best                                   60.37      28.39       0.42
kaiser_fast                                    9.89      26.29       0.39
                upsample (8 -> 16 kHz) time (ms)
                                         librosa functional transforms
sinc (width 64)                              NaN       0.79       0.41
sinc (width 16)                              NaN       0.55       0.24
kaiser_best                                20.06       0.89       0.42
kaiser_fast                                 4.32       0.69       0.26

Total running time of the script: ( 0 minutes 6.607 seconds)

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