如何使用Python中的Soundfile将具有指定SNR的高斯噪声添加到音频文件中？

Question

    print('Processing: ', filepath)
    path, file = os.path.split(filepath)
    noisy_path = path.replace('dev-clean', 'dev-noise-gassian')
    print(path, file)
    if not os.path.exists(noisy_path):
        os.makedirs(noisy_path)

    noisy_filepath = os.path.join(noisy_path, file)
    audio_signal, samplerate = sf.read(filepath)
    noise = np.random.normal(0, 0.1, audio_signal.shape[0])

    noisy_signal = audio_signal + noise

    print(audio_signal)
    print(noisy_signal)
    sf.write(noisy_filepath, noisy_signal, samplerate)

    quit()

这就是我正在做的，它增加了噪声，但我不知道噪声的信噪比是多少。如何校准添加的噪声以匹配指定的SNR？

谢谢

Answer 1

首先，一些theory

您可以通过将信号的平均功率除以噪声的平均功率来计算SNR。

对于任何给定的信号，您可以使用其power spectral density来估计其平均功率。简而言之，它是FFT的平均振幅。

下面是一个使用numpy FFT的工作示例：

import numpy as np
import soundfile as sf


sampling_rate = 42000 #42kHz sampling rate is enough for audio
Nsamples = 100000 # a bit more than 2 seconds of signal at the current sampling rate
freq = 440 # musical A
A = 5
noiseAmplitude = 5
noiseSigma = 0.1

noise = noiseAmplitude * np.random.normal(0, noiseSigma, Nsamples)

# Generate a pure sound sampled at our sampling_rate for a duration of roughly 2s
cleanSound = A*np.sin(2*np.pi*freq/sampling_rate*np.arange(Nsamples))

sampleSound = cleanSound + noise

# For a pure sine and a white noise, the theoretical SNR in dB is:
theoreticalSNR = 20*np.log10(A/(np.sqrt(2)*noiseAmplitude*noiseSigma)) # the sqrt of 2 is because of root-mean square amplitude

## Experimental measurement using FFT (we use sampling_rate//2 points for Nyquist)
# power spectrum of the clean sound (averaged spectral density)
cleanPS = np.sum(np.abs(np.fft.fft(cleanSound,sampling_rate//2)/Nsamples)**2)

# same for noise
noisePS = np.sum(np.abs(np.fft.fft(noise,sampling_rate//2)/Nsamples)**2)

# 10 instead of 20 because we're using power instead of RMS amplitude
measuredSNR = 10*np.log10(cleanPS/noisePS)

# write to output sound file
sf.write('/tmp/sample.wav',sampleSound,sampling_rate)

有了上面的值，我得到了16.989 dB的理论信噪比和16.946 dB的实测信噪比。因此，如果您想要将具有给定SNR的白噪声添加到任何给定的音频信号，您可以通过颠倒公式SNR = 10*np.log10(cleanPS/noisePS)来计算白噪声功率，并相应地选择noiseAmplitude和noiseSigma。