.. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_beginner_audio_resampling_tutorial.py: Audio Resampling ================ This tutorial shows how to use torchaudio's resampling API. .. code-block:: default import torch import torchaudio import torchaudio.functional as F import torchaudio.transforms as T print(torch.__version__) print(torchaudio.__version__) Preparation ----------- First, we import the modules and define the helper functions. .. note:: When running this tutorial in Google Colab, install the required packages with the following. .. code:: !pip install librosa .. code-block:: default import math import time import librosa import matplotlib.pyplot as plt import pandas as pd from IPython.display import Audio, display pd.set_option('display.max_rows', None) pd.set_option('display.max_columns', None) DEFAULT_OFFSET = 201 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)`. """ 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=48000, 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 in y_ticks and 1000 <= f <= sample_rate // 2] figure, axis = plt.subplots(1, 1) _, _, _, cax = 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.colorbar(cax) plt.show(block=True) Resampling Overview ------------------- To resample an audio waveform from one freqeuncy to another, you can use :py:func:`torchaudio.transforms.Resample` or :py:func:`torchaudio.functional.resample`. ``transforms.Resample`` precomputes and caches the kernel used for resampling, while ``functional.resample`` computes it on the fly, so using ``torchaudio.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. .. note:: 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. .. code-block:: default sample_rate = 48000 waveform = get_sine_sweep(sample_rate) plot_sweep(waveform, sample_rate, title="Original Waveform") Audio(waveform.numpy()[0], rate=sample_rate) Now we resample (downsample) it. We see that in the spectrogram of the resampled waveform, there is an artifact, which was not present in the original waveform. .. code-block:: default resample_rate = 32000 resampler = T.Resample(sample_rate, resample_rate, dtype=waveform.dtype) resampled_waveform = resampler(waveform) plot_sweep(resampled_waveform, resample_rate, title="Resampled Waveform") Audio(resampled_waveform.numpy()[0], rate=resample_rate) 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. .. code-block:: default 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") .. code-block:: default resampled_waveform = F.resample(waveform, sample_rate, resample_rate, lowpass_filter_width=128) plot_sweep(resampled_waveform, resample_rate, title="lowpass_filter_width=128") 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. .. code-block:: default 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") .. code-block:: default resampled_waveform = F.resample(waveform, sample_rate, resample_rate, rolloff=0.8) plot_sweep(resampled_waveform, resample_rate, title="rolloff=0.8") 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. .. code-block:: default 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") .. code-block:: default resampled_waveform = F.resample(waveform, sample_rate, resample_rate, resampling_method="kaiser_window") plot_sweep(resampled_waveform, resample_rate, title="Kaiser Window Default") 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 .. code-block:: default sample_rate = 48000 resample_rate = 32000 kaiser_best ~~~~~~~~~~~ .. code-block:: default 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)") .. code-block:: default librosa_resampled_waveform = torch.from_numpy( librosa.resample(waveform.squeeze().numpy(), orig_sr=sample_rate, target_sr=resample_rate, res_type="kaiser_best") ).unsqueeze(0) plot_sweep(librosa_resampled_waveform, resample_rate, title="Kaiser Window Best (librosa)") .. code-block:: default mse = torch.square(resampled_waveform - librosa_resampled_waveform).mean().item() print("torchaudio and librosa kaiser best MSE:", mse) kaiser_fast ~~~~~~~~~~~ .. code-block:: default resampled_waveform = F.resample( waveform, sample_rate, resample_rate, lowpass_filter_width=16, rolloff=0.85, resampling_method="kaiser_window", beta=8.555504641634386, ) plot_sweep(resampled_waveform, resample_rate, title="Kaiser Window Fast (torchaudio)") .. code-block:: default librosa_resampled_waveform = torch.from_numpy( librosa.resample(waveform.squeeze().numpy(), orig_sr=sample_rate, target_sr=resample_rate, res_type="kaiser_fast") ).unsqueeze(0) plot_sweep(librosa_resampled_waveform, resample_rate, title="Kaiser Window Fast (librosa)") .. code-block:: default mse = torch.square(resampled_waveform - librosa_resampled_waveform).mean().item() print("torchaudio and librosa kaiser fast MSE:", mse) 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. .. code-block:: default def benchmark_resample( method, waveform, sample_rate, resample_rate, lowpass_filter_width=6, rolloff=0.99, resampling_method="sinc_interpolation", beta=None, librosa_type=None, iters=5, ): if method == "functional": begin = time.monotonic() 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.monotonic() - 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.monotonic() for _ in range(iters): resampler(waveform) elapsed = time.monotonic() - begin return elapsed / iters elif method == "librosa": waveform_np = waveform.squeeze().numpy() begin = time.monotonic() for _ in range(iters): librosa.resample(waveform_np, orig_sr=sample_rate, target_sr=resample_rate, res_type=librosa_type) elapsed = time.monotonic() - begin return elapsed / iters .. code-block:: default 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("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("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("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("kaiser_fast") df = pd.DataFrame(times, columns=["librosa", "functional", "transforms"], index=rows) df.columns = pd.MultiIndex.from_product([[f"{label} time (ms)"], df.columns]) print(f"torchaudio: {torchaudio.__version__}") print(f"librosa: {librosa.__version__}") display(df.round(2)) .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.000 seconds) .. _sphx_glr_download_beginner_audio_resampling_tutorial.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download :download:`Download Python source code: audio_resampling_tutorial.py ` .. container:: sphx-glr-download :download:`Download Jupyter notebook: audio_resampling_tutorial.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_