梅尔频谱(mel

频谱(mel"/>

梅尔频谱(mel

在语音分析，合成，转换中，第一步往往是提取语音特征参数。
利用机器学习方法进行上述语音任务，常用到梅尔频谱。
本文介绍从音频文件提取梅尔频谱，和从梅尔频谱变成音频波形。

从音频波形提取Mel频谱：

1. 对音频信号预加重、分帧和加窗
2. 对每帧信号进行短时傅立叶变换STFT，得到短时幅度谱
3. 短时幅度谱通过Mel滤波器组得到Mel频谱

从Mel频谱重建音频波形

1. Mel频谱转换成幅度谱
2. griffin_lim声码器算法重建波形
3. 去加重

声码器有很多种，比如world,straight等，但是griffin_lim是特殊的，它不需要相位信息就可以重频谱重建波形，实际上它根据帧之间的关系估计相位信息。和成的音频质量也较高，代码也比较简单。

音频波形 到 mel-spectrogram

sr = 24000 # Sample rate.
n_fft = 2048 # fft points (samples)
frame_shift = 0.0125 # seconds
frame_length = 0.05 # seconds
hop_length = int(sr*frame_shift) # samples.
win_length = int(sr*frame_length) # samples.
n_mels = 512 # Number of Mel banks to generate
power = 1.2 # Exponent for amplifying the predicted magnitude
n_iter = 100 # Number of inversion iterations
preemphasis = .97 # or None
max_db = 100
ref_db = 20
top_db = 15

def get_spectrograms(fpath):'''Returns normalized log(melspectrogram) and log(magnitude) from `sound_file`.Args:sound_file: A string. The full path of a sound file.Returns:mel: A 2d array of shape (T, n_mels) <- Transposedmag: A 2d array of shape (T, 1+n_fft/2) <- Transposed'''# Loading sound filey, sr = librosa.load(fpath, sr=sr)# Trimmingy, _ = librosa.effects.trim(y, top_db=top_db)# Preemphasisy = np.append(y[0], y[1:] - preemphasis * y[:-1])# stftlinear = librosa.stft(y=y,n_fft=n_fft,hop_length=hop_length,win_length=win_length)# magnitude spectrogrammag = np.abs(linear)  # (1+n_fft//2, T)# mel spectrogrammel_basis = librosa.filters.mel(sr, n_fft, n_mels)  # (n_mels, 1+n_fft//2)mel = np.dot(mel_basis, mag)  # (n_mels, t)# to decibelmel = 20 * np.log10(np.maximum(1e-5, mel))mag = 20 * np.log10(np.maximum(1e-5, mag))# normalizemel = np.clip((mel - ref_db + max_db) / max_db, 1e-8, 1)mag = np.clip((mag - ref_db + max_db) / max_db, 1e-8, 1)# Transposemel = mel.T.astype(np.float32)  # (T, n_mels)mag = mag.T.astype(np.float32)  # (T, 1+n_fft//2)return mel, mag

mel-spectrogram 到 音频波形

def melspectrogram2wav(mel):'''# Generate wave file from spectrogram'''# transposemel = mel.T# de-noramlizemel = (np.clip(mel, 0, 1) * max_db) - max_db + ref_db# to amplitudemel = np.power(10.0, mel * 0.05)m = _mel_to_linear_matrix(sr, n_fft, n_mels)mag = np.dot(m, mel)# wav reconstructionwav = griffin_lim(mag)# de-preemphasiswav = signal.lfilter([1], [1, -preemphasis], wav)# trimwav, _ = librosa.effects.trim(wav)return wav.astype(np.float32)def spectrogram2wav(mag):'''# Generate wave file from spectrogram'''# transposemag = mag.T# de-noramlizemag = (np.clip(mag, 0, 1) * max_db) - max_db + ref_db# to amplitudemag = np.power(10.0, mag * 0.05)# wav reconstructionwav = griffin_lim(mag)# de-preemphasiswav = signal.lfilter([1], [1, -preemphasis], wav)# trimwav, _ = librosa.effects.trim(wav)return wav.astype(np.float32)

几个辅助函数：

def _mel_to_linear_matrix(sr, n_fft, n_mels):m = librosa.filters.mel(sr, n_fft, n_mels)m_t = np.transpose(m)p = np.matmul(m, m_t)d = [1.0 / x if np.abs(x) > 1.0e-8 else x for x in np.sum(p, axis=0)]return np.matmul(m_t, np.diag(d))def griffin_lim(spectrogram):'''Applies Griffin-Lim's raw.'''X_best = copy.deepcopy(spectrogram)for i in range(n_iter):X_t = invert_spectrogram(X_best)est = librosa.stft(X_t, n_fft, hop_length, win_length=win_length)phase = est / np.maximum(1e-8, np.abs(est))X_best = spectrogram * phaseX_t = invert_spectrogram(X_best)y = np.real(X_t)return ydef invert_spectrogram(spectrogram):'''spectrogram: [f, t]'''return librosa.istft(spectrogram, hop_length, win_length=win_length, window="hann")

预加重：
语音信号的平均功率谱受声门激励和口鼻辐射影响，高频端约在800HZ以上按6dB/倍频程衰落，预加重的目的是提升高频成分，使信号频谱平坦化，以便于频谱分析或声道参数分析．