减法合成

作者: Moto Hira

本教程是滤波器设计教程的延续。

本教程展示了如何使用 TorchAudio 的 DSP 函数执行减法合成。

减法合成通过对源波形应用滤波器来创建音色。

警告

本教程需要原型 DSP 特性，这些特性在 nightly build 中可用。

请参阅https://pytorch.ac.cn/get-started/locally以获取安装 nightly build 的说明。

import torch
import torchaudio

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

2.6.0
2.6.0

概述

try:
    from torchaudio.prototype.functional import filter_waveform, frequency_impulse_response, sinc_impulse_response
except ModuleNotFoundError:
    print(
        "Failed to import prototype DSP features. "
        "Please install torchaudio nightly builds. "
        "Please refer to https://pytorch.ac.cn/get-started/locally "
        "for instructions to install a nightly build."
    )
    raise

import matplotlib.pyplot as plt
from IPython.display import Audio

滤波噪声

减法合成从波形开始，并对某些频率分量应用滤波器。

对于减法合成的第一个示例，我们对白噪声应用时变低通滤波器。

首先，我们创建一个白噪声。

SAMPLE_RATE = 16_000
duration = 4
num_frames = int(duration * SAMPLE_RATE)

noise = torch.rand((num_frames,)) - 0.5

def plot_input():
    fig, axes = plt.subplots(2, 1, sharex=True)
    t = torch.linspace(0, duration, num_frames)
    axes[0].plot(t, noise)
    axes[0].grid(True)
    axes[1].specgram(noise, Fs=SAMPLE_RATE)
    Audio(noise, rate=SAMPLE_RATE)


plot_input()

窗函数-sinc 滤波器

扫描截止频率

我们使用sinc_impulse_response()创建一系列低通滤波器，同时将截止频率从零更改为奈奎斯特频率。

num_filters = 64 * duration
window_size = 2049

f_cutoff = torch.linspace(0.0, 0.8, num_filters)
kernel = sinc_impulse_response(f_cutoff, window_size)

要应用时变滤波器，我们使用filter_waveform()

filtered = filter_waveform(noise, kernel)

让我们看看结果音频的频谱图并听一下。

def plot_sinc_ir(waveform, cutoff, sample_rate, vol=0.2):
    num_frames = waveform.size(0)
    duration = num_frames / sample_rate
    num_cutoff = cutoff.size(0)
    nyquist = sample_rate / 2

    _, axes = plt.subplots(2, 1, sharex=True)
    t = torch.linspace(0, duration, num_frames)
    axes[0].plot(t, waveform)
    axes[0].grid(True)
    axes[1].specgram(waveform, Fs=sample_rate, scale="dB")
    t = torch.linspace(0, duration, num_cutoff)
    axes[1].plot(t, cutoff * nyquist, color="gray", linewidth=0.8, label="Cutoff Frequency", linestyle="--")
    axes[1].legend(loc="upper center")
    axes[1].set_ylim([0, nyquist])
    waveform /= waveform.abs().max()
    return Audio(vol * waveform, rate=sample_rate, normalize=False)

plot_sinc_ir(filtered, f_cutoff, SAMPLE_RATE)

振荡截止频率

通过振荡截止频率，我们可以模拟低频振荡 (LFO) 的效果。

PI2 = torch.pi * 2
num_filters = 90 * duration

f_lfo = torch.linspace(0.9, 0.1, num_filters)
f_cutoff_osci = torch.linspace(0.01, 0.03, num_filters) * torch.sin(torch.cumsum(f_lfo, dim=0))
f_cutoff_base = torch.linspace(0.8, 0.03, num_filters) ** 1.7
f_cutoff = f_cutoff_base + f_cutoff_osci

kernel = sinc_impulse_response(f_cutoff, window_size)
filtered = filter_waveform(noise, kernel)

plot_sinc_ir(filtered, f_cutoff, SAMPLE_RATE)

哇音效果

哇音效果是低通滤波器或带通滤波器的应用。它们快速更改截止频率或 Q 因子。

f_lfo = torch.linspace(0.15, 0.15, num_filters)
f_cutoff = 0.07 + 0.06 * torch.sin(torch.cumsum(f_lfo, dim=0))

kernel = sinc_impulse_response(f_cutoff, window_size)
filtered = filter_waveform(noise, kernel)

plot_sinc_ir(filtered, f_cutoff, SAMPLE_RATE)

任意频率响应

通过使用frequency_impulse_response()，可以直接控制频率上的功率分布。

magnitudes = torch.sin(torch.linspace(0, 10, 64)) ** 4.0
kernel = frequency_impulse_response(magnitudes)
filtered = filter_waveform(noise, kernel.unsqueeze(0))

def plot_waveform(magnitudes, filtered, sample_rate):
    nyquist = sample_rate / 2
    num_samples = filtered.size(-1)
    duration = num_samples / sample_rate

    # Re-organize magnitudes for overlay
    N = 10  # number of overlays
    interval = torch.linspace(0.05, 0.95, N)
    offsets = duration * interval
    # Select N magnitudes for overlays
    mags = torch.stack(
        [magnitudes for _ in range(N)]
        if magnitudes.ndim == 1
        else [magnitudes[int(i * magnitudes.size(0))] for i in interval]
    )
    mag_x = offsets.unsqueeze(-1) + 0.1 * mags
    mag_y = torch.linspace(0, nyquist, magnitudes.size(-1)).tile((N, 1))

    _, ax = plt.subplots(1, 1, sharex=True)
    ax.vlines(offsets, 0, nyquist, color="gray", linestyle="--", linewidth=0.8)
    ax.plot(mag_x.T.numpy(), mag_y.T.numpy(), color="gray", linewidth=0.8)
    ax.specgram(filtered, Fs=sample_rate)
    return Audio(filtered, rate=sample_rate)

plot_waveform(magnitudes, filtered, SAMPLE_RATE)

也可以制作非稳态滤波器。

magnitudes = torch.stack([torch.linspace(0.0, w, 1000) for w in torch.linspace(4.0, 40.0, 250)])
magnitudes = torch.sin(magnitudes) ** 4.0

kernel = frequency_impulse_response(magnitudes)
filtered = filter_waveform(noise, kernel)

plot_waveform(magnitudes, filtered, SAMPLE_RATE)

当然，也可以模拟简单的低通滤波器。

magnitudes = torch.concat([torch.ones((32,)), torch.zeros((32,))])

kernel = frequency_impulse_response(magnitudes)
filtered = filter_waveform(noise, kernel.unsqueeze(0))

plot_waveform(magnitudes, filtered, SAMPLE_RATE)

参考

• https://en.wikipedia.org/wiki/Additive_synthesis

• https://computermusicresource.com/Simple.bell.tutorial.html

• https://computermusicresource.com/Definitions/additive.synthesis.html