梅尔倒谱系数MFCC怎么实现

""" @author: zoutai @file: mymfcc.py @time: 2018/03/26 @description: """ from matplotlib.colors import BoundaryNorm import librosa import librosa.display import numpy import scipy.io.wavfile from scipy.fftpack import dct import matplotlib.pyplot as plt import numpy as np # 第一步-读取音频，画出时域图（采样率-幅度） sample_rate, signal = scipy.io.wavfile.read('OSR_us_000_0010_8k.wav') # File assumed to be in the same directory signal = signal[0:int(3.5 * sample_rate)] # plot the wave time = np.arange(0,len(signal))*(1.0 / sample_rate) # plt.plot(time,signal) plt.xlabel("Time(s)") plt.ylabel("Amplitude") plt.title("Signal in the Time Domain ") plt.grid('on')#标尺，on：有，off:无。 # 第二步-预加重 # 消除高频信号。因为高频信号往往都是相似的， # 通过前后时间相减，就可以近乎抹去高频信号，留下低频信号。 # 原理：y(t)=x(t)−αx(t−1) pre_emphasis = 0.97 emphasized_signal = numpy.append(signal[0], signal[1:] - pre_emphasis * signal[:-1]) time = np.arange(0,len(emphasized_signal))*(1.0 / sample_rate) # plt.plot(time,emphasized_signal) # plt.xlabel("Time(s)") # plt.ylabel("Amplitude") # plt.title("Signal in the Time Domain after Pre-Emphasis") # plt.grid('on')#标尺，on：有，off:无。 # 第三步、取帧，用帧表示 frame_size = 0.025 # 帧长 frame_stride = 0.01 # 步长 # frame_length-一帧对应的采样数, frame_step-一个步长对应的采样数 frame_length, frame_step = frame_size * sample_rate, frame_stride * sample_rate # Convert from seconds to samples signal_length = len(emphasized_signal) # 总的采样数 frame_length = int(round(frame_length)) frame_step = int(round(frame_step)) # 总帧数 num_frames = int(numpy.ceil(float(numpy.abs(signal_length - frame_length)) / frame_step)) # Make sure that we have at least 1 frame pad_signal_length = num_frames * frame_step + frame_length z = numpy.zeros((pad_signal_length - signal_length)) pad_signal = numpy.append(emphasized_signal, z) # Pad Signal to make sure that all frames have equal number of samples without truncating any samples from the original signal # Construct an array by repeating A（200） the number of times given by reps（348）. # 这个写法太妙了。目的：用矩阵来表示帧的次数，348*200，348-总的帧数，200-每一帧的采样数 # 第一帧采样为0、1、2...200;第二帧为80、81、81...280..依次类推 indices = numpy.tile(numpy.arange(0, frame_length), (num_frames, 1)) + numpy.tile(numpy.arange(0, num_frames * frame_step, frame_step), (frame_length, 1)).T frames = pad_signal[indices.astype(numpy.int32, copy=False)] # Copy of the array indices # frame：348*200，横坐标348为帧数，即时间；纵坐标200为一帧的200毫秒时间，内部数值代表信号幅度 # plt.matshow(frames, cmap='hot') # plt.colorbar() # plt.figure() # plt.pcolormesh(frames) # 第四步、加汉明窗 # 傅里叶变换默认操作的时间段内前后端点是连续的，即整个时间段刚好是一个周期， # 但是，显示却不是这样的。所以，当这种情况出现时，仍然采用FFT操作时， # 就会将单一频率周期信号认作成多个不同的频率信号的叠加，而不是原始频率，这样就差生了频谱泄漏问题 frames *= numpy.hamming(frame_length) # 相乘，和卷积类似 # # frames *= 0.54 - 0.46 * numpy.cos((2 * numpy.pi * n) / (frame_length - 1)) # Explicit Implementation ** # plt.pcolormesh(frames) # 第五步-傅里叶变换频谱和能量谱 # _raw_fft扫窗重叠，将348*200，扩展成348*512 NFFT = 512 mag_frames = numpy.absolute(numpy.fft.rfft(frames, NFFT)) # Magnitude of the FFT pow_frames = ((1.0 / NFFT) * ((mag_frames) ** 2)) # Power Spectrum # plt.pcolormesh(mag_frames) # # plt.pcolormesh(pow_frames) # 第六步，Filter Banks滤波器组 # 公式：m=2595*log10(1+f/700)；f=700(10^(m/2595)−1) nfilt = 40 #窗的数目 low_freq_mel = 0 high_freq_mel = (2595 * numpy.log10(1 + (sample_rate / 2) / 700)) # Convert Hz to Mel mel_points = numpy.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 = numpy.floor((NFFT + 1) * hz_points / sample_rate) fbank = numpy.zeros((nfilt, int(numpy.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]) filter_banks = numpy.dot(pow_frames, fbank.T) filter_banks = numpy.where(filter_banks == 0, numpy.finfo(float).eps, filter_banks) # Numerical Stability filter_banks = 20 * numpy.log10(filter_banks) # dB;348*26 # plt.subplot(111) # plt.pcolormesh(filter_banks.T) # plt.grid('on') # plt.ylabel('Frequency [Hz]') # plt.xlabel('Time [sec]') # plt.show() # # 第七步，梅尔频谱倒谱系数-MFCCs num_ceps = 12 #取12个系数 cep_lifter=22 #倒谱的升个数？？ mfcc = dct(filter_banks, type=2, axis=1, norm='ortho')[:, 1 : (num_ceps + 1)] # Keep 2-13 (nframes, ncoeff) = mfcc.shape n = numpy.arange(ncoeff) lift = 1 + (cep_lifter / 2) * numpy.sin(numpy.pi * n / cep_lifter) mfcc *= lift #* # plt.pcolormesh(mfcc.T) # plt.ylabel('Frequency [Hz]') # plt.xlabel('Time [sec]') # 第八步，均值化优化 # to balance the spectrum and improve the Signal-to-Noise (SNR), we can simply subtract the mean of each coefficient from all frames. filter_banks -= (numpy.mean(filter_banks, axis=0) + 1e-8) mfcc -= (numpy.mean(mfcc, axis=0) + 1e-8) # plt.subplot(111) # plt.pcolormesh(mfcc.T) # plt.ylabel('Frequency [Hz]') # plt.xlabel('Time [sec]') # plt.show() # 直接频谱分析 # plot the wave # plt.specgram(signal,Fs = sample_rate, scale_by_freq = True, sides = 'default') # plt.ylabel('Frequency(Hz)') # plt.xlabel('Time(s)') # plt.show() plt.figure(figsize=(10, 4)) mfccs = librosa.feature.melspectrogram(signal,sr=8000,n_fft=512,n_mels=40) librosa.display.specshow(mfccs, x_axis='time') plt.colorbar() plt.title('MFCC') plt.tight_layout() plt.show()

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