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音频重采样

译者:龙琰

项目地址:https://pytorch.apachecn.org/2.0/tutorials/beginner/audio_resampling_tutorial

原始地址:https://pytorch.org/audio/stable/tutorials/audio_resampling_tutorial.html

作者: Caroline Chen, Moto Hira

本教程展示如何使用 torchaudio 的重采样 API。

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

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

输出:

2.3.0
2.3.0

准备工作

首先,我们导入模块并定义辅助函数。

import math
import timeit

import librosa
import matplotlib.colors as mcolors
import matplotlib.pyplot as plt
import pandas as pd
import resampy
from IPython.display import Audio

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
    times, 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
                times.append(t)
                freq.append(f)
    t_max = _get_inverse_log_freq(f_max, sample_rate, offset) / sample_rate
    times.append(t_max)
    freq.append(f_max)
    return times, 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)

重采样概述

要将音频波形从一种频率重新采样为另一种频率,可以使用 torchaudio.transforms.Resampletorchaudio.functional.resample()transforms.Resample 预先计算并缓存用于重采样的内核,而 functional.resample 则动态计算它,因此使用 torchaudio.transforms.Resample 将在使用相同参数重采样多个波形时加快速度(请参阅基准测试部分)。

两种重采样方法都使用带限正弦插值来计算任意时间步长的信号值。 实现涉及卷积,因此我们可以利用 GPU/多线程来提高性能。

Note

在多个子进程中使用重采样时(例如使用多个工作进程加载数据),您的应用程序可能会创建比系统能够有效处理的线程更多的线程。 在这种情况下,设置 torch.set_num_threads(1) 可能会有所帮助。

由于有限数量的样本只能代表有限数量的频率,因此重采样不会产生完美的结果,并且可以使用多种参数来控制其质量和计算速度。 我们通过对对数正弦扫描重新采样来演示这些特性,这是一种频率随时间呈指数增长的正弦波。

下面的频谱图显示了信号的频率表示,其中 x 轴对应于原始波形的频率(以对数刻度表示),y 轴对应于绘制波形的频率,颜色强度对应于幅度。

sample_rate = 48000
waveform = get_sine_sweep(sample_rate)

plot_sweep(waveform, sample_rate, title="Original Waveform")
Audio(waveform.numpy()[0], rate=sample_rate)

Original Waveform (sample rate: 48000 Hz)

我们看到,在重采样波形的频谱图中,存在原始波形中不存在的伪影。

这种效应称为混叠。 本页解释了它是如何发生的,以及为什么它看起来像反射。

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)

Original Waveform (sample rate: 48000 Hz)

使用参数控制重采样质量

Lowpass filter width

由于用于插值的滤波器无限扩展,因此 lowpass_filter_width 参数用于控制用于对插值进行加窗的滤波器的宽度。 它也称为过零数,因为插值在每个时间单位都经过零。 使用较大的 lowpass_filter_width 可提供更清晰、更精确的滤波器,但计算成本更高。

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")

Original Waveform (sample rate: 48000 Hz)

resampled_waveform = F.resample(waveform, sample_rate, resample_rate, lowpass_filter_width=128)
plot_sweep(resampled_waveform, resample_rate, title="lowpass_filter_width=128")

Original Waveform (sample rate: 48000 Hz)

Rolloff

rolloff 参数表示为奈奎斯特频率的一个小数,奈奎斯特频率是给定的有限采样率所能表示的最大频率。rolloff 决定了 lowpass filter 的截止,并控制混叠的程度,当高于奈奎斯特的频率映射到较低的频率时,就会发生混叠。因此,较低的 rolloff 将减少混叠的数量,但它也将减少一些较高的频率。

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")

Original Waveform (sample rate: 48000 Hz)

resampled_waveform = F.resample(waveform, sample_rate, resample_rate, rolloff=0.8)
plot_sweep(resampled_waveform, resample_rate, title="rolloff=0.8")

Original Waveform (sample rate: 48000 Hz)

窗口函数

默认情况下,torchaudio 的重采样使用 Hann 窗口滤波器,这是一个加权余弦函数。它还支持凯泽窗(Kaiser window),这是一个近乎最优的窗函数,它包含一个额外的 beta 参数,用于设计滤波器的平滑性和脉冲宽度。这可以使用 resampling_method 参数来控制。

sample_rate = 48000
resample_rate = 32000

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

Original Waveform (sample rate: 48000 Hz)

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

Original Waveform (sample rate: 48000 Hz)

与 librosa 比较

torchaudio 的重采样函数可用于产生类似于 librosa (resampy) 的 kaiser 窗口重采样的结果,但有一些噪声

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="sinc_interp_kaiser",
    beta=14.769656459379492,
)
plot_sweep(resampled_waveform, resample_rate, title="Kaiser Window Best (torchaudio)")

Original Waveform (sample rate: 48000 Hz)

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)")

Original Waveform (sample rate: 48000 Hz)

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

输出:

torchaudio and librosa kaiser best MSE: 2.0806901153660115e-06

kaiser_fast

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

Original Waveform (sample rate: 48000 Hz)

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)")

Original Waveform (sample rate: 48000 Hz)

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

输出:

torchaudio and librosa kaiser fast MSE: 2.5200744248601437e-05

性能基准测试

下面是两对采样率之间的下采样和上采样波形的基准。我们展示了 lowpass_filter_width、窗口类型和采样率可能产生的性能影响。使用 torchaudio 中相应的参数,与 librosakaiser_bestkaiser_fast 进行比较。

print(f"torchaudio: {torchaudio.__version__}")
print(f"librosa: {librosa.__version__}")
print(f"resampy: {resampy.__version__}")

输出:

torchaudio: 2.3.0
librosa: 0.10.0
resampy: 0.2.2
def benchmark_resample_functional(
    waveform,
    sample_rate,
    resample_rate,
    lowpass_filter_width=6,
    rolloff=0.99,
    resampling_method="sinc_interp_hann",
    beta=None,
    iters=5,
):
    return (
        timeit.timeit(
            stmt="""
torchaudio.functional.resample(
    waveform,
    sample_rate,
    resample_rate,
    lowpass_filter_width=lowpass_filter_width,
    rolloff=rolloff,
    resampling_method=resampling_method,
    beta=beta,
)
        """,
            setup="import torchaudio",
            number=iters,
            globals=locals(),
        )
        * 1000
        / iters
    )
def benchmark_resample_transforms(
    waveform,
    sample_rate,
    resample_rate,
    lowpass_filter_width=6,
    rolloff=0.99,
    resampling_method="sinc_interp_hann",
    beta=None,
    iters=5,
):
    return (
        timeit.timeit(
            stmt="resampler(waveform)",
            setup="""
import torchaudio

resampler = torchaudio.transforms.Resample(
    sample_rate,
    resample_rate,
    lowpass_filter_width=lowpass_filter_width,
    rolloff=rolloff,
    resampling_method=resampling_method,
    dtype=waveform.dtype,
    beta=beta,
)
resampler.to(waveform.device)
        """,
            number=iters,
            globals=locals(),
        )
        * 1000
        / iters
    )
def benchmark_resample_librosa(
    waveform,
    sample_rate,
    resample_rate,
    res_type=None,
    iters=5,
):
    waveform_np = waveform.squeeze().numpy()
    return (
        timeit.timeit(
            stmt="""
librosa.resample(
    waveform_np,
    orig_sr=sample_rate,
    target_sr=resample_rate,
    res_type=res_type,
)
        """,
            setup="import librosa",
            number=iters,
            globals=locals(),
        )
        * 1000
        / iters
    )
def benchmark(sample_rate, resample_rate):
    times, rows = [], []
    waveform = get_sine_sweep(sample_rate).to(torch.float32)

    args = (waveform, sample_rate, resample_rate)

    # sinc 64 zero-crossings
    f_time = benchmark_resample_functional(*args, lowpass_filter_width=64)
    t_time = benchmark_resample_transforms(*args, lowpass_filter_width=64)
    times.append([None, f_time, t_time])
    rows.append("sinc (width 64)")

    # sinc 6 zero-crossings
    f_time = benchmark_resample_functional(*args, lowpass_filter_width=16)
    t_time = benchmark_resample_transforms(*args, lowpass_filter_width=16)
    times.append([None, f_time, t_time])
    rows.append("sinc (width 16)")

    # kaiser best
    kwargs = {
        "lowpass_filter_width": 64,
        "rolloff": 0.9475937167399596,
        "resampling_method": "sinc_interp_kaiser",
        "beta": 14.769656459379492,
    }
    lib_time = benchmark_resample_librosa(*args, res_type="kaiser_best")
    f_time = benchmark_resample_functional(*args, **kwargs)
    t_time = benchmark_resample_transforms(*args, **kwargs)
    times.append([lib_time, f_time, t_time])
    rows.append("kaiser_best")

    # kaiser fast
    kwargs = {
        "lowpass_filter_width": 16,
        "rolloff": 0.85,
        "resampling_method": "sinc_interp_kaiser",
        "beta": 8.555504641634386,
    }
    lib_time = benchmark_resample_librosa(*args, res_type="kaiser_fast")
    f_time = benchmark_resample_functional(*args, **kwargs)
    t_time = benchmark_resample_transforms(*args, **kwargs)
    times.append([lib_time, f_time, t_time])
    rows.append("kaiser_fast")

    df = pd.DataFrame(times, columns=["librosa", "functional", "transforms"], index=rows)
    return df
def plot(df):
    print(df.round(2))
    ax = df.plot(kind="bar")
    plt.ylabel("Time Elapsed [ms]")
    plt.xticks(rotation=0, fontsize=10)
    for cont, col, color in zip(ax.containers, df.columns, mcolors.TABLEAU_COLORS):
        label = ["N/A" if v != v else str(v) for v in df[col].round(2)]
        ax.bar_label(cont, labels=label, color=color, fontweight="bold", fontsize="x-small")

下采样 (48 -> 44.1 kHz)

df = benchmark(48_000, 44_100)
plot(df)

audio resampling tutorial

                 librosa  functional  transforms
sinc (width 64)      NaN        0.86        0.39
sinc (width 16)      NaN        0.70        0.34
kaiser_best        85.02        1.32        0.39
kaiser_fast         8.05        1.18        0.35

下采样 (16 -> 8 kHz)

df = benchmark(16_000, 8_000)
plot(df)

audio resampling tutorial

                 librosa  functional  transforms
sinc (width 64)      NaN        1.30        1.11
sinc (width 16)      NaN        0.53        0.37
kaiser_best        11.25        1.39        1.17
kaiser_fast         3.14        0.58        0.40

上采样 (44.1 -> 48 kHz)

df = benchmark(44_100, 48_000)
plot(df)

audio resampling tutorial

输出:

                 librosa  functional  transforms
sinc (width 64)      NaN        0.84        0.36
sinc (width 16)      NaN        0.70        0.33
kaiser_best        32.57        1.09        0.35
kaiser_fast         7.86        0.92        0.33

上采样 (8 -> 16 kHz)

df = benchmark(8_000, 16_000)
plot(df)

audio resampling tutorial

输出:

                 librosa  functional  transforms
sinc (width 64)      NaN        0.69        0.49
sinc (width 16)      NaN        0.37        0.22
kaiser_best        11.20        0.72        0.50
kaiser_fast         2.97        0.41        0.24

总结

详细说明结果:

  • 较大的 lowpass_filter_width 会导致较大的重采样内核,因此会增加内核计算和卷积的计算时间

  • 使用 sinc_interp_kaiser 会导致比默认的 sinc_interp_hann 更长的计算时间,因为计算中间窗口值更复杂

  • 采样率和重采样率之间的大 GCD 将导致简化,从而允许更小的内核和更快的内核计算。

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