计算MFCC特征的自相关系数实现代码

以下是使用Python实现计算MFCC特征的自相关系数的代码：

import numpy as np
from scipy.fftpack import dct

def mfcc(signal, sample_rate=16000, num_ceps=13, nfilt=26, nfft=512):
    # Pre-emphasis
    pre_emphasis = 0.97
    emphasized_signal = np.append(signal[0], signal[1:] - pre_emphasis * signal[:-1])

    # Framing
    frame_size = 0.025
    frame_stride = 0.01
    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)]

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

    # Fourier-transform and power spectrum
    mag_frames = np.absolute(np.fft.rfft(frames, nfft))  # Magnitude of the FFT
    pow_frames = ((1.0 / nfft) * ((mag_frames) ** 2))  # Power Spectrum

    # Filter banks
    low_freq_mel = 0
    high_freq_mel = (2595 * np.log10(1 + (sample_rate / 2) / 700))  # Convert Hz to Mel
    mel_points = np.linspace(low_freq_mel, high_freq_mel, nfilt + 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)

    fbank = np.zeros((nfilt, int(np.floor(nfft / 2 + 1))))
    for m in range(1, nfilt + 1):
        f_m_minus = int(bin[m - 1])   # left
        f_m = int(bin[m])             # center
        f_m_plus = int(bin[m + 1])    # right

        for k in range(f_m_minus, f_m):
            fbank[m - 1, k] = (k - bin[m - 1]) / (bin[m] - bin[m - 1])
        for k in range(f_m, f_m_plus):
            fbank[m - 1, k] = (bin[m + 1] - k) / (bin[m + 1] - bin[m])

    # Apply filter banks
    filtered_frames = np.dot(pow_frames, fbank.T)
    filtered_frames = np.where(filtered_frames == 0, np.finfo(float).eps, filtered_frames)  # Numerical Stability
    filtered_frames = 20 * np.log10(filtered_frames)  # dB

    # MFCCs
    mfccs = dct(filtered_frames, type=2, axis=1, norm='ortho')[:, 1 : (num_ceps + 1)]

    # Mean normalization
    mfccs -= (np.mean(mfccs, axis=0) + 1e-8)

    # Compute autocorrelation
    mfccs_ac = np.zeros_like(mfccs)
    for i in range(num_ceps):
        for j in range(num_ceps):
            mfccs_ac[i, j] = np.mean(np.multiply(mfccs[:, i], mfccs[:, j]))

    return mfccs_ac.flatten()

在该代码中，我们首先对输入的信号进行预加重、分帧、加窗、傅里叶变换和滤波器组处理，得到MFCC系数。然后，我们对MFCC系数进行均值归一化，并计算自相关系数。最后，我们将自相关系数展平为一维数组并返回。