在Python中获取对数Mel谱图

的过程可以通过以下步骤实现：

导入所需的库：

import numpy as np
import scipy.io.wavfile as wav
from scipy.fftpack import dct
from scipy.signal import lfilter
import matplotlib.pyplot as plt

定义函数get_mel_spectrum，该函数用于计算对数Mel谱图：

def get_mel_spectrum(signal, sample_rate, frame_size=0.025, frame_stride=0.01, num_filters=26, num_ceps=13, low_freq=0, high_freq=None):
    # 预加重处理
    pre_emphasis = 0.97
    emphasized_signal = np.append(signal[0], signal[1:] - pre_emphasis * signal[:-1])

    # 分帧
    frame_length = int(round(frame_size * sample_rate))
    frame_step = int(round(frame_stride * sample_rate))
    signal_length = len(emphasized_signal)
    num_frames = int(np.ceil(float(np.abs(signal_length - frame_length)) / frame_step))

    pad_signal_length = num_frames * frame_step + frame_length
    z = np.zeros((pad_signal_length - signal_length))
    pad_signal = np.append(emphasized_signal, z)

    indices = np.tile(np.arange(0, frame_length), (num_frames, 1)) + np.tile(np.arange(0, num_frames * frame_step, frame_step), (frame_length, 1)).T
    frames = pad_signal[indices.astype(np.int32, copy=False)]

    # 加窗
    hamming_window = np.hamming(frame_length)
    frames *= hamming_window

    # 快速傅里叶变换
    NFFT = 512
    mag_frames = np.absolute(np.fft.rfft(frames, NFFT))  # Magnitude of the FFT

    # Mel滤波器
    low_freq_mel = (2595 * np.log10(1 + low_freq / 700))  # Convert Hz to Mel
    high_freq_mel = (2595 * np.log10(1 + high_freq / 700)) if high_freq else (sample_rate / 2)  # Convert Hz to Mel
    mel_points = np.linspace(low_freq_mel, high_freq_mel, num_filters + 2)  # Equally spaced in Mel scale
    hz_points = (700 * (10**(mel_points / 2595) - 1))  # Convert Mel to Hz
    bin = np.floor((NFFT + 1) * hz_points / sample_rate).astype(int)

    filters = np.zeros((num_filters, int(np.floor(NFFT / 2 + 1))))
    for m in range(1, num_filters + 1):
        filters[m - 1, bin[m - 1]:bin[m]] = (hz_points[m] - hz_points[m - 1]) / (bin[m] - bin[m - 1])  # Left slope
        filters[m - 1, bin[m]:bin[m + 1]] = (hz_points[m + 1] - hz_points[m]) / (bin[m + 1] - bin[m])  # Right slope

    # Mel滤波器应用
    mel_spectrum = np.dot(mag_frames, filters.T)
    mel_spectrum = np.where(mel_spectrum == 0, np.finfo(float).eps, mel_spectrum)  # Avoid zero division
    mel_spectrum = 20 * np.log10(mel_spectrum)  # dB

    # Cepstral系数计算
    dct_filter = dct(mel_spectrum, type=2, axis=1, norm='ortho')[:, :num_ceps]

    return dct_filter

调用get_mel_spectrum函数并绘制对数Mel谱图：

# 加载音频文件
sample_rate, signal = wav.read("audio.wav")

# 获取对数Mel谱图
mel_spectrum = get_mel_spectrum(signal, sample_rate)

# 绘制对数Mel谱图
plt.imshow(mel_spectrum.T, cmap='hot', origin='lower', aspect='auto')
plt.xlabel('Frame')
plt.ylabel('Mel Filter')
plt.title('Log Mel Spectrogram')
plt.colorbar(format='%+2.0f dB')
plt.tight_layout()
plt.show()

以上代码中，假设音频文件为"audio.wav"，需要提前准备好。

对数Mel谱图可以通过将音频信号进行预加重、分帧、加窗、快速傅里叶变换、Mel滤波器应用、对数化等一系列处理得到。这种谱图常用于语音识别、音频信号处理等领域。

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